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	8112s	Isogeny class
Conductor	8112	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	316368 = 24 · 32 · 133	Discriminant
Eigenvalues	2+ 3-  0 -2 -2 13- -2  6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-43,92]	[a1,a2,a3,a4,a6]
Generators	[8:18:1]	Generators of the group modulo torsion
j	256000/9	j-invariant
L	4.7472928001353	L(r)(E,1)/r!
Ω	3.0358634682027	Real period
R	1.5637372529621	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	4056o1 32448ct1 24336t1 8112r1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 8112s1

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 8112s1

-4	8	-3	13
4056o1	32448ct1	24336t1	8112r1

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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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