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	8112g	Isogeny class
Conductor	8112	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1152	Modular degree for the optimal curve
Δ	-1687296 = -1 · 28 · 3 · 133	Discriminant
Eigenvalues	2+ 3+ -2 -2 -4 13- -6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-4,64]	[a1,a2,a3,a4,a6]
Generators	[0:8:1] [5:12:1]	Generators of the group modulo torsion
j	-16/3	j-invariant
L	4.322476400594	L(r)(E,1)/r!
Ω	2.1710909919712	Real period
R	1.9909236492523	Regulator
r	2	Rank of the group of rational points
S	0.99999999999998	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	4056r1 32448dj1 24336u1 8112f1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 8112g1

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	-4	-	-6	-2	-4	6	-2	-8	6	-4	-8	2	-8	-14	-14	-12	-4	0	0	-6	12

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Quadratic twists for elliptic curve 8112g1

-4	8	-3	13
4056r1	32448dj1	24336u1	8112f1

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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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