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	7605d	Isogeny class
Conductor	7605	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	1152	Modular degree for the optimal curve
Δ	-1482975 = -1 · 33 · 52 · 133	Discriminant
Eigenvalues	-1 3+ 5+ -4  0 13- -4 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,7,56]	[a1,a2,a3,a4,a6]
Generators	[-2:6:1] [0:7:1]	Generators of the group modulo torsion
j	729/25	j-invariant
L	3.3317779766649	L(r)(E,1)/r!
Ω	2.0285457996203	Real period
R	0.8212232568992	Regulator
r	2	Rank of the group of rational points
S	0.99999999999945	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	121680co1 7605h1 38025n1 7605g1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 7605d1

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	+	+	-4	0	-	-4	-4	-8	-8	4	-4	2	-8	8	-12	0	-2	-12	4	-4	-8	12	-18	4

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Quadratic twists for elliptic curve 7605d1

-4	-3	5	13
121680co1	7605h1	38025n1	7605g1

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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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