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	651b	Isogeny class
Conductor	651	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-141267 = -1 · 3 · 72 · 312	Discriminant
Eigenvalues	1 3+  4 7-  2 -2  2  8	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,12,15]	[a1,a2,a3,a4,a6]
j	167284151/141267	j-invariant
L	2.1187478668053	L(r)(E,1)/r!
Ω	2.1187478668053	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	10416bi2 41664bz2 1953f2 16275o2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 651b2

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	+	4	-	2	-2	2	8	-6	0	+	6	8	-4	-2	4	-6	-6	-4	4	-10	12	-16	2	-10

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Quadratic twists for elliptic curve 651b2

-4	8	-3	5	-7	-11	13	-31
10416bi2	41664bz2	1953f2	16275o2	4557o2	78771c2	110019h2	20181n2

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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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