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	8112b	Isogeny class
Conductor	8112	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	5376	Modular degree for the optimal curve
Δ	81322078032 = 24 · 34 · 137	Discriminant
Eigenvalues	2+ 3+ -2  0  0 13+  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1239,-9270]	[a1,a2,a3,a4,a6]
Generators	[438:9126:1]	Generators of the group modulo torsion
j	2725888/1053	j-invariant
L	3.023955775427	L(r)(E,1)/r!
Ω	0.83143949587408	Real period
R	1.818506211476	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	4056f1 32448da1 24336f1 624c1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 8112b1

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	0	0	+	2	-4	0	6	0	2	-6	12	-4	6	-8	-2	4	-12	14	0	8	18	6

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Quadratic twists for elliptic curve 8112b1

-4	8	-3	13
4056f1	32448da1	24336f1	624c1

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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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