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	10640r	Isogeny class
Conductor	10640	Conductor
∏ cp	14	Product of Tamagawa factors cp
deg	64512	Modular degree for the optimal curve
Δ	-21001473370357760 = -1 · 228 · 5 · 77 · 19	Discriminant
Eigenvalues	2-  1 5+ 7-  0  4  7 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,40264,-6227116]	[a1,a2,a3,a4,a6]
j	1762396940073671/5127312834560	j-invariant
L	2.7515489895415	L(r)(E,1)/r!
Ω	0.19653921353868	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	1330a1 42560de1 95760fi1 53200bv1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 10640r1

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	+	-	0	4	7	-	5	2	4	-5	-5	1	0	-5	14	-4	-14	7	5	-4	16	-10	10

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Quadratic twists for elliptic curve 10640r1

-4	8	-3	5	-7
1330a1	42560de1	95760fi1	53200bv1	74480ch1

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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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