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	8112r	Isogeny class
Conductor	8112	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	9984	Modular degree for the optimal curve
Δ	1527047909712 = 24 · 32 · 139	Discriminant
Eigenvalues	2+ 3-  0  2  2 13- -2 -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-7323,231336]	[a1,a2,a3,a4,a6]
Generators	[110298:12951315:8]	Generators of the group modulo torsion
j	256000/9	j-invariant
L	5.4912540178303	L(r)(E,1)/r!
Ω	0.84199703076253	Real period
R	6.5217023542913	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	4056e1 32448cs1 24336s1 8112s1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 8112r1

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

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Quadratic twists for elliptic curve 8112r1

-4	8	-3	13
4056e1	32448cs1	24336s1	8112s1

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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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