It does not say that the sword Beowulf used to defeat Grendel's dam was a magical one.
http://www.humanities.mcmaster.ca/~beowulf/main.html
Chapter XXIII
'MID the battle-gear saw he a blade triumphant,
old-sword of Eotens, with edge of proof,
warriors' heirloom, weapon unmatched,
-- save only 'twas more than other men
to bandy-of-battle could bear at all --
as the giants had wrought it, ready and keen.
Seized then its chain-hilt the Scyldings' chieftain,
bold and battle-grim, brandished the sword,
reckless of life, and so wrathfully smote
that it gripped her neck and grasped her hard,
her bone-rings breaking: the blade pierced through
that fated-one's flesh: to floor she sank.
Bloody the blade: he was blithe of his deed.
Then blazed forth light. 'Twas bright within
as when from the sky there shines unclouded
heaven's candle. The hall he scanned.
By the wall then went he; his weapon raised
high by its hilts the Hygelac-thane,
angry and eager. That edge was not useless
to the warrior now.
...
Now that sword began,
from blood of the fight, in battle-droppings,3
war-blade, to wane: 'twas a wondrous thing
that all of it melted as ice is wont
when frosty fetters the Father loosens,
unwinds the wave-bonds, wielding all
seasons and times: the true God he!
Nor took from that dwelling the duke of the Geats
precious things, though a plenty he saw,
save only the head and that hilt withal
blazoned with jewels: the blade had melted,
burned was the bright sword, her blood was so hot,
so poisoned the hell-sprite who perished within there.