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	7605g	Isogeny class
Conductor	7605	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	178950926919375 = 33 · 54 · 139	Discriminant
Eigenvalues	1 3+ 5-  4  0 13- -4  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-31719,2084850]	[a1,a2,a3,a4,a6]
Generators	[66:492:1]	Generators of the group modulo torsion
j	12326391/625	j-invariant
L	5.9136950494472	L(r)(E,1)/r!
Ω	0.56261737655062	Real period
R	2.6277605775811	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	121680dc2 7605c2 38025q2 7605d2	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 7605g2

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 7605g2

-4	-3	5	13
121680dc2	7605c2	38025q2	7605d2

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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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