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	72	Product of Tamagawa factors cp
Δ	10434657678665472 = 28 · 38 · 7 · 316	Discriminant
Eigenvalues	2- 3-  0 7-  0 -4  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-268455,53311102]	[a1,a2,a3,a4,a6]
Generators	[26279:4259214:1]	Generators of the group modulo torsion
j	11464911586546000/55912731903	j-invariant
L	4.3211030870426	L(r)(E,1)/r!
Ω	0.4082839783778	Real period
R	5.2917862515831	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	31248bh4 124992cz4 2604f4 54684j4	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 7812j4

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 7812j4

-4	8	-3	-7
31248bh4	124992cz4	2604f4	54684j4

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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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