Cremona's table of elliptic curves

7497 = 3² · 7² · 17

Field	Data	Notes
Atkin-Lehner	3- 7- 17+	Signs for the Atkin-Lehner involutions
Class	7497g	Isogeny class
Conductor	7497	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	2048	Modular degree for the optimal curve
Δ	-38257191 = -1 · 38 · 73 · 17	Discriminant
Eigenvalues	-1 3- -2 7-  6  4 17+  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-41,-304]	[a1,a2,a3,a4,a6]
Generators	[18:58:1]	Generators of the group modulo torsion
j	-29791/153	j-invariant
L	2.5071586855253	L(r)(E,1)/r!
Ω	0.85215412265613	Real period
R	1.471071147148	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	119952fi1 2499m1 7497p1 127449bl1	Quadratic twists by: -4 -3 -7 17

Hecke Eigenvalues for elliptic curve 7497g1

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
-1	-	-2	-	6	4	+	2	-6	-8	4	2	-10	4	-12	-2	12	-14	4	14	6	8	-4	2	-14

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Quadratic twists for elliptic curve 7497g1

-4	-3	-7	17
119952fi1	2499m1	7497p1	127449bl1

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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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