Cremona's table of elliptic curves

8112 = 2⁴ · 3 · 13²

Field	Data	Notes
Atkin-Lehner	2- 3+ 13-	Signs for the Atkin-Lehner involutions
Class	8112y	Isogeny class
Conductor	8112	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-28308129447936 = -1 · 232 · 3 · 133	Discriminant
Eigenvalues	2- 3+ -2  2  0 13-  2 -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-70984,-7260176]	[a1,a2,a3,a4,a6]
Generators	[598605444:30571626496:226981]	Generators of the group modulo torsion
j	-4395631034341/3145728	j-invariant
L	3.3060862324447	L(r)(E,1)/r!
Ω	0.14623801800378	Real period
R	11.303785012866	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	1014c3 32448di3 24336cc3 8112w3	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 8112y3

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

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Quadratic twists for elliptic curve 8112y3

-4	8	-3	13
1014c3	32448di3	24336cc3	8112w3

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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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