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	2385i	Isogeny class
Conductor	2385	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	640	Modular degree for the optimal curve
Δ	15647985 = 310 · 5 · 53	Discriminant
Eigenvalues	-1 3- 5-  4  4 -2  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-77,-156]	[a1,a2,a3,a4,a6]
j	68417929/21465	j-invariant
L	1.6530635162666	L(r)(E,1)/r!
Ω	1.6530635162666	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	38160ck1 795a1 11925n1 116865w1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2385i1

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	-	-	4	4	-2	2	4	8	10	-8	-2	-6	0	8	-	-4	-10	-12	-12	6	-8	-12	6	18

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Quadratic twists for elliptic curve 2385i1

-4	-3	5	-7	53
38160ck1	795a1	11925n1	116865w1	126405p1

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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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