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	10640be	Isogeny class
Conductor	10640	Conductor
∏ cp	14	Product of Tamagawa factors cp
deg	13440	Modular degree for the optimal curve
Δ	-1361920000000 = -1 · 217 · 57 · 7 · 19	Discriminant
Eigenvalues	2-  2 5- 7- -1 -3 -7 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1120,-57600]	[a1,a2,a3,a4,a6]
Generators	[90:750:1]	Generators of the group modulo torsion
j	-37966934881/332500000	j-invariant
L	6.6428995659954	L(r)(E,1)/r!
Ω	0.36172805803126	Real period
R	1.3117390691919	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	1330i1 42560cm1 95760dr1 53200bz1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 10640be1

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	-3	-7	-	-1	1	4	-4	-5	8	2	-4	-5	-1	1	11	-14	-11	9	6	2

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Quadratic twists for elliptic curve 10640be1

-4	8	-3	5	-7
1330i1	42560cm1	95760dr1	53200bz1	74480bk1

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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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