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	97344df	Isogeny class
Conductor	97344	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	944669786112 = 216 · 38 · 133	Discriminant
Eigenvalues	2+ 3- -2  2  4 13-  6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-9516,354224]	[a1,a2,a3,a4,a6]
Generators	[-104:468:1]	Generators of the group modulo torsion
j	907924/9	j-invariant
L	7.1632359077291	L(r)(E,1)/r!
Ω	0.88634418591374	Real period
R	2.0204442047002	Regulator
r	1	Rank of the group of rational points
S	1.0000000017496	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	97344gl2 12168j2 32448o2 97344dd2	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 97344df2

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	4	-	6	-2	-4	6	2	8	-6	-4	-8	2	8	14	-14	-12	-4	0	0	6	12

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Quadratic twists for elliptic curve 97344df2

-4	8	-3	13
97344gl2	12168j2	32448o2	97344dd2

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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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