Cremona's table of elliptic curves

8281 = 7² · 13²

Field	Data	Notes
Atkin-Lehner	7+ 13+	Signs for the Atkin-Lehner involutions
Class	8281c	Isogeny class
Conductor	8281	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	5544	Modular degree for the optimal curve
Δ	974251369 = 78 · 132	Discriminant
Eigenvalues	-1 -3 -3 7+  3 13+ -2  1	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-279,-906]	[a1,a2,a3,a4,a6]
Generators	[-12:30:1]	Generators of the group modulo torsion
j	2457	j-invariant
L	1.1093009497492	L(r)(E,1)/r!
Ω	1.210765109712	Real period
R	0.30539943733402	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	74529n1 8281h1 8281a1	Quadratic twists by: -3 -7 13

Hecke Eigenvalues for elliptic curve 8281c1

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
-1	-3	-3	+	3	+	-2	1	0	7	-3	-2	-3	-7	-1	3	4	-13	3	-13	13	-3	0	-6	5

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Quadratic twists for elliptic curve 8281c1

-3	-7	13
74529n1	8281h1	8281a1

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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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