Cremona's table of elliptic curves

7455 = 3 · 5 · 7 · 71

Field	Data	Notes
Atkin-Lehner	3+ 5+ 7- 71-	Signs for the Atkin-Lehner involutions
Class	7455a	Isogeny class
Conductor	7455	Conductor
∏ cp	10	Product of Tamagawa factors cp
deg	53280	Modular degree for the optimal curve
Δ	-108739189125 = -1 · 36 · 53 · 75 · 71	Discriminant
Eigenvalues	1 3+ 5+ 7- -5  0  4 -1	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-783328,266521657]	[a1,a2,a3,a4,a6]
Generators	[544:1051:1]	Generators of the group modulo torsion
j	-53156396270339108473609/108739189125	j-invariant
L	3.7107534540067	L(r)(E,1)/r!
Ω	0.6874372225812	Real period
R	0.53979524705884	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	119280ca1 22365l1 37275i1 52185n1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 7455a1

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	+	+	-	-5	0	4	-1	6	-1	4	0	-3	-3	-9	14	10	11	-6	-	-13	-4	6	-16	-16

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Quadratic twists for elliptic curve 7455a1

-4	-3	5	-7
119280ca1	22365l1	37275i1	52185n1

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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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