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	1638t	Isogeny class
Conductor	1638	Conductor
∏ cp	324	Product of Tamagawa factors cp
Δ	-7594259452416 = -1 · 29 · 39 · 73 · 133	Discriminant
Eigenvalues	2- 3- -3 7- -3 13-  3 -7	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-1094,133589]	[a1,a2,a3,a4,a6]
Generators	[-27:391:1]	Generators of the group modulo torsion
j	-198461344537/10417365504	j-invariant
L	3.5793626035194	L(r)(E,1)/r!
Ω	0.61437641127669	Real period
R	0.16183358794658	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	13104by2 52416cq2 546d2 40950w2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1638t2

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
-	-	-3	-	-3	-	3	-7	-9	9	-4	-7	-12	-1	0	6	-12	-1	14	-12	-7	-10	6	6	-10

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Quadratic twists for elliptic curve 1638t2

-4	8	-3	5	-7	13
13104by2	52416cq2	546d2	40950w2	11466cc2	21294t2

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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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