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	7497b	Isogeny class
Conductor	7497	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	2880	Modular degree for the optimal curve
Δ	-54000891 = -1 · 33 · 76 · 17	Discriminant
Eigenvalues	-2 3+  1 7- -3  5 17-  1	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-147,-772]	[a1,a2,a3,a4,a6]
Generators	[21:73:1]	Generators of the group modulo torsion
j	-110592/17	j-invariant
L	2.2932058513309	L(r)(E,1)/r!
Ω	0.67979153749979	Real period
R	0.84334892567398	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	119952cx1 7497a1 153a1 127449l1	Quadratic twists by: -4 -3 -7 17

Hecke Eigenvalues for elliptic curve 7497b1

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	+	1	-	-3	5	-	1	-7	6	-4	10	-9	1	12	-12	-6	-2	4	-8	0	-6	-4	-2	-8

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Quadratic twists for elliptic curve 7497b1

-4	-3	-7	17
119952cx1	7497a1	153a1	127449l1

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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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