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	7605q	Isogeny class
Conductor	7605	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	178136402900625 = 310 · 54 · 136	Discriminant
Eigenvalues	-1 3- 5-  0 -4 13+ -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-15242,338784]	[a1,a2,a3,a4,a6]
Generators	[-58:1041:1]	Generators of the group modulo torsion
j	111284641/50625	j-invariant
L	2.5920412169462	L(r)(E,1)/r!
Ω	0.51120664011138	Real period
R	1.2676093254488	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	121680en3 2535a3 38025bc3 45a4	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 7605q4

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

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Quadratic twists for elliptic curve 7605q4

-4	-3	5	13
121680en3	2535a3	38025bc3	45a4

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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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