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	16	Product of Tamagawa factors cp
Δ	216790749 = 37 · 73 · 172	Discriminant
Eigenvalues	-1 3- -2 7-  6  4 17+  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-986,-11644]	[a1,a2,a3,a4,a6]
Generators	[-18:13:1]	Generators of the group modulo torsion
j	423564751/867	j-invariant
L	2.5071586855253	L(r)(E,1)/r!
Ω	0.85215412265613	Real period
R	0.735535573574	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	119952fi2 2499m2 7497p2 127449bl2	Quadratic twists by: -4 -3 -7 17

Hecke Eigenvalues for elliptic curve 7497g2

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 7497g2

-4	-3	-7	17
119952fi2	2499m2	7497p2	127449bl2

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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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