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	10640p	Isogeny class
Conductor	10640	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	40320	Modular degree for the optimal curve
Δ	-2226394122158080 = -1 · 219 · 5 · 73 · 195	Discriminant
Eigenvalues	2-  0 5+ 7-  1 -1 -3 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-56843,-5688902]	[a1,a2,a3,a4,a6]
Generators	[447:7630:1]	Generators of the group modulo torsion
j	-4959007166945889/543553252480	j-invariant
L	4.0423702835752	L(r)(E,1)/r!
Ω	0.15364693519185	Real period
R	4.3849125903787	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	1330g1 42560dh1 95760fc1 53200bk1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 10640p1

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
-	0	+	-	1	-1	-3	+	5	-9	2	10	-3	6	12	8	3	-9	-3	-9	2	-7	7	-10	-8

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Quadratic twists for elliptic curve 10640p1

-4	8	-3	5	-7
1330g1	42560dh1	95760fc1	53200bk1	74480cp1

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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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