Cremona's table of elliptic curves

3735 = 3² · 5 · 83

Field	Data	Notes
Atkin-Lehner	3- 5+ 83-	Signs for the Atkin-Lehner involutions
Class	3735c	Isogeny class
Conductor	3735	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	24960	Modular degree for the optimal curve
Δ	12211896181640625 = 37 · 510 · 833	Discriminant
Eigenvalues	1 3- 5+  0 -2  4  4 -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-312255,67027576]	[a1,a2,a3,a4,a6]
Generators	[500:5726:1]	Generators of the group modulo torsion
j	4618757595675440881/16751572265625	j-invariant
L	4.009747900321	L(r)(E,1)/r!
Ω	0.40266631201058	Real period
R	1.6596653278077	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	59760w1 1245b1 18675h1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 3735c1

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	-	+	0	-2	4	4	-2	0	2	0	2	2	4	-8	-14	-14	-14	0	-16	-8	6	-	-6	8

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Quadratic twists for elliptic curve 3735c1

-4	-3	5
59760w1	1245b1	18675h1

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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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