Cremona's table of elliptic curves

10640 = 2⁴ · 5 · 7 · 19

Field	Data	Notes
Atkin-Lehner	2- 5- 7- 19-	Signs for the Atkin-Lehner involutions
Class	10640bc	Isogeny class
Conductor	10640	Conductor
∏ cp	52	Product of Tamagawa factors cp
deg	37440	Modular degree for the optimal curve
Δ	-789687500000000 = -1 · 28 · 513 · 7 · 192	Discriminant
Eigenvalues	2- -1 5- 7- -3 -5 -1 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,2275,1350625]	[a1,a2,a3,a4,a6]
Generators	[825:23750:1]	Generators of the group modulo torsion
j	5084368707584/3084716796875	j-invariant
L	3.6206486767322	L(r)(E,1)/r!
Ω	0.39240673305157	Real period
R	0.17743798284617	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	2660e1 42560ck1 95760dx1 53200bu1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 10640bc1

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	-5	-1	-	4	-3	8	4	-8	-4	1	12	14	10	12	8	-6	1	-4	-14	1

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Quadratic twists for elliptic curve 10640bc1

-4	8	-3	5	-7
2660e1	42560ck1	95760dx1	53200bu1	74480bf1

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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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