Cremona's table of elliptic curves

7605 = 3² · 5 · 13²

Field	Data	Notes
Atkin-Lehner	3- 5+ 13-	Signs for the Atkin-Lehner involutions
Class	7605m	Isogeny class
Conductor	7605	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	3456	Modular degree for the optimal curve
Δ	-5405443875 = -1 · 39 · 53 · 133	Discriminant
Eigenvalues	0 3- 5+ -3 -3 13-  3  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,312,-2831]	[a1,a2,a3,a4,a6]
Generators	[13:58:1]	Generators of the group modulo torsion
j	2097152/3375	j-invariant
L	2.5441312912692	L(r)(E,1)/r!
Ω	0.71540296236168	Real period
R	0.88905533843144	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	121680ek1 2535d1 38025bw1 7605u1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 7605m1

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	-	+	-3	-3	-	3	0	-3	6	-6	9	-3	10	-12	3	12	1	0	9	-6	1	6	15	-9

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Quadratic twists for elliptic curve 7605m1

-4	-3	5	13
121680ek1	2535d1	38025bw1	7605u1

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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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