Cremona's table of elliptic curves

2385 = 3² · 5 · 53

Field	Data	Notes
Atkin-Lehner	3+ 5+ 53+	Signs for the Atkin-Lehner involutions
Class	2385a	Isogeny class
Conductor	2385	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1584	Modular degree for the optimal curve
Δ	-130399875 = -1 · 39 · 53 · 53	Discriminant
Eigenvalues	2 3+ 5+ -4  6  0 -3  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,27,-547]	[a1,a2,a3,a4,a6]
Generators	[162:725:8]	Generators of the group modulo torsion
j	110592/6625	j-invariant
L	5.2822345464858	L(r)(E,1)/r!
Ω	0.88376667400608	Real period
R	2.9884780122686	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	38160q1 2385d1 11925f1 116865h1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2385a1

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	+	+	-4	6	0	-3	4	-8	-10	-8	2	-9	-2	7	+	10	-8	-3	7	-7	-10	-16	10	10

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Quadratic twists for elliptic curve 2385a1

-4	-3	5	-7	53
38160q1	2385d1	11925f1	116865h1	126405g1

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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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