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	48	Product of Tamagawa factors cp
Δ	-25046451847872 = -1 · 26 · 39 · 76 · 132	Discriminant
Eigenvalues	2+ 3+  0 7-  0 13- -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,6708,-116848]	[a1,a2,a3,a4,a6]
Generators	[64:724:1]	Generators of the group modulo torsion
j	1695802078125/1272491584	j-invariant
L	2.205037763062	L(r)(E,1)/r!
Ω	0.37558587747285	Real period
R	0.4892440263149	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	13104bg4 52416p4 1638m2 40950cw4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1638c4

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 1638c4

-4	8	-3	5	-7	13
13104bg4	52416p4	1638m2	40950cw4	11466b4	21294bm4

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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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