Cremona's table of elliptic curves

3610 = 2 · 5 · 19²

Field	Data	Notes
Atkin-Lehner	2- 5+ 19-	Signs for the Atkin-Lehner involutions
Class	3610g	Isogeny class
Conductor	3610	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	2880	Modular degree for the optimal curve
Δ	-44693586950 = -1 · 2 · 52 · 197	Discriminant
Eigenvalues	2-  1 5+ -1  0  3 -7 19-	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,534,-8950]	[a1,a2,a3,a4,a6]
Generators	[734:6853:8]	Generators of the group modulo torsion
j	357911/950	j-invariant
L	5.3946260355615	L(r)(E,1)/r!
Ω	0.58579217726333	Real period
R	2.3022781137006	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	28880u1 115520y1 32490u1 18050h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3610g1

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	+	-1	0	3	-7	-	-5	5	-10	-2	-2	6	0	-9	7	-4	-7	0	-9	10	-2	10	18

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Quadratic twists for elliptic curve 3610g1

-4	8	-3	5	-19
28880u1	115520y1	32490u1	18050h1	190b1

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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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