Cremona's table of elliptic curves

7812 = 2² · 3² · 7 · 31

Field	Data	Notes
Atkin-Lehner	2- 3- 7- 31-	Signs for the Atkin-Lehner involutions
Class	7812j	Isogeny class
Conductor	7812	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	44844845246208 = 28 · 312 · 73 · 312	Discriminant
Eigenvalues	2- 3-  0 7-  0 -4  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-18975,-953066]	[a1,a2,a3,a4,a6]
Generators	[278:3906:1]	Generators of the group modulo torsion
j	4048569250000/240295167	j-invariant
L	4.3211030870426	L(r)(E,1)/r!
Ω	0.4082839783778	Real period
R	1.7639287505277	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	31248bh2 124992cz2 2604f2 54684j2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 7812j2

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

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Quadratic twists for elliptic curve 7812j2

-4	8	-3	-7
31248bh2	124992cz2	2604f2	54684j2

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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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