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	7605c	Isogeny class
Conductor	7605	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	130455225724224375 = 39 · 54 · 139	Discriminant
Eigenvalues	-1 3+ 5+  4  0 13-  4  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-285473,-56005478]	[a1,a2,a3,a4,a6]
j	12326391/625	j-invariant
L	1.6575407394806	L(r)(E,1)/r!
Ω	0.20719259243507	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	121680cp2 7605g2 38025o2 7605h2	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 7605c2

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 7605c2

-4	-3	5	13
121680cp2	7605g2	38025o2	7605h2

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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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