Cremona's table of elliptic curves

651 = 3 · 7 · 31

Field	Data	Notes
Atkin-Lehner	3- 7+ 31-	Signs for the Atkin-Lehner involutions
Class	651c	Isogeny class
Conductor	651	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	32	Modular degree for the optimal curve
Δ	-13671 = -1 · 32 · 72 · 31	Discriminant
Eigenvalues	1 3- -2 7+ -2 -4  0 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,3,-5]	[a1,a2,a3,a4,a6]
Generators	[5:9:1]	Generators of the group modulo torsion
j	4657463/13671	j-invariant
L	2.6338964694672	L(r)(E,1)/r!
Ω	2.036256416952	Real period
R	1.2934994078053	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	10416ba1 41664k1 1953c1 16275j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 651c1

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	-	-2	+	-2	-4	0	-4	2	-2	-	-2	6	-2	-8	2	-4	-4	0	12	4	-2	8	0	-2

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Quadratic twists for elliptic curve 651c1

-4	8	-3	5	-7	-11	13	-31
10416ba1	41664k1	1953c1	16275j1	4557c1	78771v1	110019t1	20181c1

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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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