Cremona's table of elliptic curves

9758 = 2 · 7 · 17 · 41

Field	Data	Notes
Atkin-Lehner	2- 7+ 17+ 41+	Signs for the Atkin-Lehner involutions
Class	9758g	Isogeny class
Conductor	9758	Conductor
∏ cp	72	Product of Tamagawa factors cp
Δ	12187976192 = 29 · 72 · 172 · 412	Discriminant
Eigenvalues	2- -2 -2 7+ -4 -2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-2629,51393]	[a1,a2,a3,a4,a6]
Generators	[-44:309:1] [-2:239:1]	Generators of the group modulo torsion
j	2009582291311057/12187976192	j-invariant
L	5.6449228436903	L(r)(E,1)/r!
Ω	1.2747266349417	Real period
R	0.24601888440485	Regulator
r	2	Rank of the group of rational points
S	0.9999999999999	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	78064h2 87822m2 68306z2	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 9758g2

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	-2	+	-4	-4	-6	-8	-8	+	-4	0	0	14	6	-2	-8	-10	-8	-6	-18	-2

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Quadratic twists for elliptic curve 9758g2

-4	-3	-7
78064h2	87822m2	68306z2

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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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