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	1638m	Isogeny class
Conductor	1638	Conductor
∏ cp	72	Product of Tamagawa factors cp
deg	576	Modular degree for the optimal curve
Δ	493129728 = 212 · 33 · 73 · 13	Discriminant
Eigenvalues	2- 3+  0 7-  0 13-  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-215,623]	[a1,a2,a3,a4,a6]
j	40530337875/18264064	j-invariant
L	2.9733272296676	L(r)(E,1)/r!
Ω	1.4866636148338	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	13104bf1 52416o1 1638c3 40950b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1638m1

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

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Quadratic twists for elliptic curve 1638m1

-4	8	-3	5	-7	13
13104bf1	52416o1	1638c3	40950b1	11466bj1	21294a1

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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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