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	1638c	Isogeny class
Conductor	1638	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	576	Modular degree for the optimal curve
Δ	6643728 = 24 · 33 · 7 · 133	Discriminant
Eigenvalues	2+ 3+  0 7-  0 13- -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-957,11637]	[a1,a2,a3,a4,a6]
Generators	[-9:144:1]	Generators of the group modulo torsion
j	3592121380875/246064	j-invariant
L	2.205037763062	L(r)(E,1)/r!
Ω	2.2535152648371	Real period
R	2.9354641578894	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	13104bg1 52416p1 1638m3 40950cw1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1638c1

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 1638c1

-4	8	-3	5	-7	13
13104bg1	52416p1	1638m3	40950cw1	11466b1	21294bm1

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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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