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	97344c	Isogeny class
Conductor	97344	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-97286227504128 = -1 · 210 · 39 · 136	Discriminant
Eigenvalues	2+ 3+  0  4  0 13+  0  8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,0,-474552]	[a1,a2,a3,a4,a6]
Generators	[282490:4697693:1000]	Generators of the group modulo torsion
j	0	j-invariant
L	8.6362072421644	L(r)(E,1)/r!
Ω	0.27499053525635	Real period
R	7.8513677120074	Regulator
r	1	Rank of the group of rational points
S	1.0000000004269	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	97344ds3 6084a3 97344c1 576a3	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 97344c3

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	4	0	+	0	8	0	0	4	-10	0	-8	0	0	0	-14	-16	0	10	-4	0	0	-14

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Quadratic twists for elliptic curve 97344c3

-4	8	-3	13
97344ds3	6084a3	97344c1	576a3

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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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