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	7497i	Isogeny class
Conductor	7497	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	43008	Modular degree for the optimal curve
Δ	-156246232020291 = -1 · 313 · 78 · 17	Discriminant
Eigenvalues	2 3- -3 7-  3 -1 17+  7	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-18669,1151365]	[a1,a2,a3,a4,a6]
Generators	[770:3965:8]	Generators of the group modulo torsion
j	-8390176768/1821771	j-invariant
L	6.908143339741	L(r)(E,1)/r!
Ω	0.55120496581426	Real period
R	3.1332007910778	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	119952fq1 2499g1 1071d1 127449bo1	Quadratic twists by: -4 -3 -7 17

Hecke Eigenvalues for elliptic curve 7497i1

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	-	-3	-	3	-1	+	7	-1	10	-4	-10	3	-11	-8	4	4	-10	-8	-8	2	16	6	-8	4

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Quadratic twists for elliptic curve 7497i1

-4	-3	-7	17
119952fq1	2499g1	1071d1	127449bo1

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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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