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	8112c	Isogeny class
Conductor	8112	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	19968	Modular degree for the optimal curve
Δ	-67659968922624 = -1 · 210 · 34 · 138	Discriminant
Eigenvalues	2+ 3+  3  0  0 13+ -1  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,8056,-284064]	[a1,a2,a3,a4,a6]
Generators	[110:1386:1]	Generators of the group modulo torsion
j	69212/81	j-invariant
L	4.4397510570253	L(r)(E,1)/r!
Ω	0.33232904295971	Real period
R	3.3398759084407	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	4056g1 32448de1 24336o1 8112d1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 8112c1

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
+	+	3	0	0	+	-1	0	-4	3	-8	-5	3	-4	8	-13	-12	15	-12	-8	3	4	-12	10	2

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Quadratic twists for elliptic curve 8112c1

-4	8	-3	13
4056g1	32448de1	24336o1	8112d1

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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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