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	3610i	Isogeny class
Conductor	3610	Conductor
∏ cp	136	Product of Tamagawa factors cp
deg	5440	Modular degree for the optimal curve
Δ	-561889280000 = -1 · 217 · 54 · 193	Discriminant
Eigenvalues	2- -1 5- -3  2  5 -5 19+	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,1655,-24393]	[a1,a2,a3,a4,a6]
Generators	[207:-3144:1]	Generators of the group modulo torsion
j	73087061741/81920000	j-invariant
L	4.3229562618777	L(r)(E,1)/r!
Ω	0.49690987479063	Real period
R	0.063968225858732	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	28880bb1 115520c1 32490i1 18050c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3610i1

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	2	5	-5	+	-3	-7	-2	-10	0	10	0	-3	-13	12	11	-12	1	-4	-6	-6	-12

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Quadratic twists for elliptic curve 3610i1

-4	8	-3	5	-19
28880bb1	115520c1	32490i1	18050c1	3610d1

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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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