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	8112bg	Isogeny class
Conductor	8112	Conductor
∏ cp	40	Product of Tamagawa factors cp
Δ	2195430671601303552 = 216 · 35 · 1310	Discriminant
Eigenvalues	2- 3- -2  4 -4 13+  2 -8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-56079664,-161661424300]	[a1,a2,a3,a4,a6]
Generators	[-4324510:104307:1000]	Generators of the group modulo torsion
j	986551739719628473/111045168	j-invariant
L	4.8858898220498	L(r)(E,1)/r!
Ω	0.055169393072635	Real period
R	8.8561601821814	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	1014e4 32448cg4 24336bs4 624i3	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 8112bg3

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	4	-4	+	2	-8	0	6	-4	2	10	-4	8	-10	4	-2	-16	-8	-2	-8	12	-14	-10

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Quadratic twists for elliptic curve 8112bg3

-4	8	-3	13
1014e4	32448cg4	24336bs4	624i3

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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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