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	97344ep	Isogeny class
Conductor	97344	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	172032	Modular degree for the optimal curve
Δ	114176197556928 = 26 · 37 · 138	Discriminant
Eigenvalues	2- 3-  0 -2  0 13+ -2 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-12675,-193336]	[a1,a2,a3,a4,a6]
Generators	[-670:4239:8]	Generators of the group modulo torsion
j	1000000/507	j-invariant
L	4.9219177834911	L(r)(E,1)/r!
Ω	0.47473813163366	Real period
R	5.1838239503375	Regulator
r	1	Rank of the group of rational points
S	0.99999999790509	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	97344em1 48672bn2 32448by1 7488bm1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 97344ep1

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	0	+	-2	-2	-8	6	-2	-6	0	-4	8	-6	-4	-2	2	4	2	12	12	12	18

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Quadratic twists for elliptic curve 97344ep1

-4	8	-3	13
97344em1	48672bn2	32448by1	7488bm1

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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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