Cremona's table of elliptic curves

1640 = 2³ · 5 · 41

Field	Data	Notes
Atkin-Lehner	2+ 5- 41+	Signs for the Atkin-Lehner involutions
Class	1640c	Isogeny class
Conductor	1640	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	640	Modular degree for the optimal curve
Δ	26240000 = 210 · 54 · 41	Discriminant
Eigenvalues	2+  2 5-  4  6 -4 -6  6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-80,-100]	[a1,a2,a3,a4,a6]
j	55990084/25625	j-invariant
L	3.3310886566261	L(r)(E,1)/r!
Ω	1.6655443283131	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	3280e1 13120g1 14760u1 8200i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1640c1

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	-	4	6	-4	-6	6	0	-4	8	2	+	-4	-12	-4	0	-14	-6	12	10	0	4	-6	-6

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Quadratic twists for elliptic curve 1640c1

-4	8	-3	5	-7	41
3280e1	13120g1	14760u1	8200i1	80360f1	67240g1

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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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