Cremona's table of elliptic curves

2405 = 5 · 13 · 37

Field	Data	Notes
Atkin-Lehner	5+ 13+ 37-	Signs for the Atkin-Lehner involutions
Class	2405b	Isogeny class
Conductor	2405	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	352	Modular degree for the optimal curve
Δ	156325 = 52 · 132 · 37	Discriminant
Eigenvalues	-2 -1 5+ -1 -3 13+ -8 -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-16,22]	[a1,a2,a3,a4,a6]
Generators	[-4:2:1] [-2:6:1]	Generators of the group modulo torsion
j	481890304/156325	j-invariant
L	1.7330852578094	L(r)(E,1)/r!
Ω	2.9920737097871	Real period
R	0.14480636390578	Regulator
r	2	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	38480n1 21645p1 12025d1 117845r1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2405b1

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
-2	-1	+	-1	-3	+	-8	-6	-6	0	4	-	1	-4	-9	-13	-8	8	-12	11	-13	10	1	2	-14

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Quadratic twists for elliptic curve 2405b1

-4	-3	5	-7	13	37
38480n1	21645p1	12025d1	117845r1	31265d1	88985i1

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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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