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	1640b	Isogeny class
Conductor	1640	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	160	Modular degree for the optimal curve
Δ	134480 = 24 · 5 · 412	Discriminant
Eigenvalues	2+  2 5-  2 -4  4  4  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-15,20]	[a1,a2,a3,a4,a6]
j	24918016/8405	j-invariant
L	3.021685461043	L(r)(E,1)/r!
Ω	3.021685461043	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	3280d1 13120f1 14760r1 8200h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1640b1

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

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Quadratic twists for elliptic curve 1640b1

-4	8	-3	5	-7	41
3280d1	13120f1	14760r1	8200h1	80360e1	67240f1

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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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