Cremona's table of elliptic curves

1638 = 2 · 3² · 7 · 13

Field	Data	Notes
Atkin-Lehner	2+ 3- 7- 13+	Signs for the Atkin-Lehner involutions
Class	1638i	Isogeny class
Conductor	1638	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	136525662 = 2 · 37 · 74 · 13	Discriminant
Eigenvalues	2+ 3- -2 7-  4 13+ -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-3753,-87561]	[a1,a2,a3,a4,a6]
Generators	[-35:18:1]	Generators of the group modulo torsion
j	8020417344913/187278	j-invariant
L	2.0214627052223	L(r)(E,1)/r!
Ω	0.60995823327049	Real period
R	1.6570501019255	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	13104bt3 52416dd4 546g3 40950dy4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1638i3

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	0	6	-8	10	6	4	-4	-10	-4	-6	-8	0	-10	-8	-4	6	-2

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Quadratic twists for elliptic curve 1638i3

-4	8	-3	5	-7	13
13104bt3	52416dd4	546g3	40950dy4	11466y3	21294cg4

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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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