Cremona's table of elliptic curves

9296 = 2⁴ · 7 · 83

Field	Data	Notes
Atkin-Lehner	2- 7- 83-	Signs for the Atkin-Lehner involutions
Class	9296c	Isogeny class
Conductor	9296	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	3456	Modular degree for the optimal curve
Δ	-233218048 = -1 · 213 · 73 · 83	Discriminant
Eigenvalues	2- -2 -2 7- -1 -2 -6 -1	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-344,2452]	[a1,a2,a3,a4,a6]
Generators	[-18:56:1] [-2:56:1]	Generators of the group modulo torsion
j	-1102302937/56938	j-invariant
L	4.1074015958903	L(r)(E,1)/r!
Ω	1.7424669948297	Real period
R	0.19643612610162	Regulator
r	2	Rank of the group of rational points
S	0.99999999999975	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	1162a1 37184f1 83664bx1 65072u1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 9296c1

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	-2	-	-1	-2	-6	-1	-4	-6	-7	-8	-6	4	0	-11	6	5	16	-7	11	-15	-	-17	6

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Quadratic twists for elliptic curve 9296c1

-4	8	-3	-7
1162a1	37184f1	83664bx1	65072u1

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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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