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	4	Product of Tamagawa factors cp
Δ	86067200 = 211 · 52 · 412	Discriminant
Eigenvalues	2+  2 5-  4  6 -4 -6  6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1080,-13300]	[a1,a2,a3,a4,a6]
j	68087453042/42025	j-invariant
L	3.3310886566261	L(r)(E,1)/r!
Ω	0.83277216415653	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	3280e2 13120g2 14760u2 8200i2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1640c2

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 1640c2

-4	8	-3	5	-7	41
3280e2	13120g2	14760u2	8200i2	80360f2	67240g2

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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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