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	7605f	Isogeny class
Conductor	7605	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	32256	Modular degree for the optimal curve
Δ	-771924412569375 = -1 · 39 · 54 · 137	Discriminant
Eigenvalues	1 3+ 5- -2  4 13+ -4 -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-36789,3036320]	[a1,a2,a3,a4,a6]
j	-57960603/8125	j-invariant
L	1.9530348257978	L(r)(E,1)/r!
Ω	0.48825870644945	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	121680cw1 7605b1 38025l1 585a1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 7605f1

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	4	+	-4	-6	0	-4	10	2	6	-8	8	-4	-12	2	10	0	6	12	4	-14	14

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Quadratic twists for elliptic curve 7605f1

-4	-3	5	13
121680cw1	7605b1	38025l1	585a1

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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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