Cremona's table of elliptic curves

97344 = 2⁶ · 3² · 13²

Field	Data	Notes
Atkin-Lehner	2- 3- 13+	Signs for the Atkin-Lehner involutions
Class	97344fn	Isogeny class
Conductor	97344	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	10321920	Modular degree for the optimal curve
Δ	-1.9096647016144E+23	Discriminant
Eigenvalues	2- 3- -2  4 -4 13+ -2  8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1900236,21049193360]	[a1,a2,a3,a4,a6]
Generators	[22403771:1876775589:12167]	Generators of the group modulo torsion
j	-822656953/207028224	j-invariant
L	6.3605772293223	L(r)(E,1)/r!
Ω	0.0821147644354	Real period
R	9.6824506024784	Regulator
r	1	Rank of the group of rational points
S	1.0000000041322	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	97344ci1 24336bs1 32448cg1 7488bt1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 97344fn1

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

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Quadratic twists for elliptic curve 97344fn1

-4	8	-3	13
97344ci1	24336bs1	32448cg1	7488bt1

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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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