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	7605b	Isogeny class
Conductor	7605	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	550618236675 = 33 · 52 · 138	Discriminant
Eigenvalues	-1 3+ 5+ -2 -4 13+  4 -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-67463,-6727444]	[a1,a2,a3,a4,a6]
Generators	[-150:82:1]	Generators of the group modulo torsion
j	260549802603/4225	j-invariant
L	1.9637247741365	L(r)(E,1)/r!
Ω	0.29623343036146	Real period
R	1.6572443999149	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	121680ci2 7605f2 38025i2 585c2	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 7605b2

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 7605b2

-4	-3	5	13
121680ci2	7605f2	38025i2	585c2

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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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