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	1640d	Isogeny class
Conductor	1640	Conductor
∏ cp	30	Product of Tamagawa factors cp
Δ	30400667142400000 = 211 · 55 · 416	Discriminant
Eigenvalues	2+  0 5-  2 -2 -2 -4 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-156307,22257294]	[a1,a2,a3,a4,a6]
Generators	[438:6150:1]	Generators of the group modulo torsion
j	206219174047187922/14844075753125	j-invariant
L	2.9729729362591	L(r)(E,1)/r!
Ω	0.36402721220813	Real period
R	1.0889196692103	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	3280g2 13120i2 14760o2 8200j2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1640d2

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

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Quadratic twists for elliptic curve 1640d2

-4	8	-3	5	-7	41
3280g2	13120i2	14760o2	8200j2	80360a2	67240c2

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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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