Cremona's table of elliptic curves

3185 = 5 · 7² · 13

Field	Data	Notes
Atkin-Lehner	5- 7+ 13-	Signs for the Atkin-Lehner involutions
Class	3185g	Isogeny class
Conductor	3185	Conductor
∏ cp	22	Product of Tamagawa factors cp
deg	29040	Modular degree for the optimal curve
Δ	-19812939453125 = -1 · 511 · 74 · 132	Discriminant
Eigenvalues	-1 -3 5- 7+  0 13-  0 -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-246357,47126706]	[a1,a2,a3,a4,a6]
Generators	[416:-4271:1]	Generators of the group modulo torsion
j	-688691336801860161/8251953125	j-invariant
L	1.3459697988456	L(r)(E,1)/r!
Ω	0.62208517388852	Real period
R	0.09834737744937	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	50960bl1 28665u1 15925c1 3185c1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 3185g1

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	-3	-	+	0	-	0	-6	-1	-5	-4	8	11	1	-12	10	0	-5	-1	0	12	8	13	-13	-14

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Quadratic twists for elliptic curve 3185g1

-4	-3	5	-7	13
50960bl1	28665u1	15925c1	3185c1	41405b1

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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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