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	8112d	Isogeny class
Conductor	8112	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	-14017536 = -1 · 210 · 34 · 132	Discriminant
Eigenvalues	2+ 3+ -3  0  0 13+ -1  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,48,-144]	[a1,a2,a3,a4,a6]
Generators	[6:18:1]	Generators of the group modulo torsion
j	69212/81	j-invariant
L	2.7334921968417	L(r)(E,1)/r!
Ω	1.1982294047171	Real period
R	0.57031904451698	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	4056q1 32448db1 24336m1 8112c1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 8112d1

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 8112d1

-4	8	-3	13
4056q1	32448db1	24336m1	8112c1

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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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