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	1640a	Isogeny class
Conductor	1640	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-243205337139200 = -1 · 211 · 52 · 416	Discriminant
Eigenvalues	2+  0 5-  2  4  4  2 -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-21907,1456206]	[a1,a2,a3,a4,a6]
j	-567730837600722/118752606025	j-invariant
L	2.1272704822393	L(r)(E,1)/r!
Ω	0.53181762055983	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	3280a2 13120a2 14760s2 8200g2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1640a2

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	4	4	2	-8	4	4	4	-6	+	4	-2	12	-4	10	-4	-6	6	6	-4	18	10

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Quadratic twists for elliptic curve 1640a2

-4	8	-3	5	-7	41
3280a2	13120a2	14760s2	8200g2	80360d2	67240d2

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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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