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	8112x	Isogeny class
Conductor	8112	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	1687296 = 28 · 3 · 133	Discriminant
Eigenvalues	2- 3+  2  4 -6 13-  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-212,1260]	[a1,a2,a3,a4,a6]
Generators	[90:105:8]	Generators of the group modulo torsion
j	1882384/3	j-invariant
L	4.4558622742523	L(r)(E,1)/r!
Ω	2.6572416887562	Real period
R	3.3537500883768	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	2028e2 32448dn2 24336cf2 8112z2	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 8112x2

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

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Quadratic twists for elliptic curve 8112x2

-4	8	-3	13
2028e2	32448dn2	24336cf2	8112z2

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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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