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	7497c	Isogeny class
Conductor	7497	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	33600	Modular degree for the optimal curve
Δ	-295131771593883 = -1 · 311 · 78 · 172	Discriminant
Eigenvalues	0 3- -4 7+ -4  1 17+  1	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-28812,2055856]	[a1,a2,a3,a4,a6]
Generators	[-98:1984:1] [-38:1759:1]	Generators of the group modulo torsion
j	-629407744/70227	j-invariant
L	3.9784372691634	L(r)(E,1)/r!
Ω	0.53195566754154	Real period
R	0.31162036549878	Regulator
r	2	Rank of the group of rational points
S	1.0000000000002	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	119952dt1 2499a1 7497m1 127449s1	Quadratic twists by: -4 -3 -7 17

Hecke Eigenvalues for elliptic curve 7497c1

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	+	-4	1	+	1	-2	-6	-9	-11	-10	-7	-6	6	-8	6	3	2	-9	-3	-6	0	2

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Quadratic twists for elliptic curve 7497c1

-4	-3	-7	17
119952dt1	2499a1	7497m1	127449s1

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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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