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	8112ba	Isogeny class
Conductor	8112	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	-6230016 = -1 · 212 · 32 · 132	Discriminant
Eigenvalues	2- 3-  1  2 -2 13+ -7 -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-160,-844]	[a1,a2,a3,a4,a6]
Generators	[20:66:1]	Generators of the group modulo torsion
j	-658489/9	j-invariant
L	5.5703619296183	L(r)(E,1)/r!
Ω	0.67028653961255	Real period
R	2.0776047258976	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	507b1 32448cc1 24336bm1 8112bd1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 8112ba1

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
-	-	1	2	-2	+	-7	-6	6	-1	4	-1	-9	-6	6	-9	0	1	-2	6	-11	4	-14	14	2

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Quadratic twists for elliptic curve 8112ba1

-4	8	-3	13
507b1	32448cc1	24336bm1	8112bd1

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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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