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	7497d	Isogeny class
Conductor	7497	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	8640	Modular degree for the optimal curve
Δ	2089646029611 = 311 · 74 · 173	Discriminant
Eigenvalues	1 3- -1 7+  2  1 17+ -8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-4860,111537]	[a1,a2,a3,a4,a6]
j	7253758561/1193859	j-invariant
L	1.5780028584093	L(r)(E,1)/r!
Ω	0.78900142920464	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	119952dm1 2499i1 7497n1 127449t1	Quadratic twists by: -4 -3 -7 17

Hecke Eigenvalues for elliptic curve 7497d1

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

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Quadratic twists for elliptic curve 7497d1

-4	-3	-7	17
119952dm1	2499i1	7497n1	127449t1

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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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