Cremona's table of elliptic curves

8281 = 7² · 13²

Field	Data	Notes
Atkin-Lehner	7- 13+	Signs for the Atkin-Lehner involutions
Class	8281d	Isogeny class
Conductor	8281	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-427929800129788411 = -1 · 79 · 139	Discriminant
Eigenvalues	0  2 -3 7-  0 13+  6 -7	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,104893,-28663685]	[a1,a2,a3,a4,a6]
j	224755712/753571	j-invariant
L	1.2163517835429	L(r)(E,1)/r!
Ω	0.15204397294287	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	74529v2 1183a2 637b2	Quadratic twists by: -3 -7 13

Hecke Eigenvalues for elliptic curve 8281d2

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
0	2	-3	-	0	+	6	-7	3	-9	5	-2	-6	-1	3	-9	0	10	-14	6	11	-1	3	15	-1

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Quadratic twists for elliptic curve 8281d2

-3	-7	13
74529v2	1183a2	637b2

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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