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	1638p	Isogeny class
Conductor	1638	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	960	Modular degree for the optimal curve
Δ	-1579796946 = -1 · 2 · 311 · 73 · 13	Discriminant
Eigenvalues	2- 3-  1 7+  1 13-  1  7	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-977,12147]	[a1,a2,a3,a4,a6]
j	-141339344329/2167074	j-invariant
L	3.0137993988384	L(r)(E,1)/r!
Ω	1.5068996994192	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	13104ch1 52416bm1 546a1 40950bj1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1638p1

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
-	-	1	+	1	-	1	7	-3	3	8	7	-8	7	-8	10	-4	7	2	-4	-1	2	6	-14	-14

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Quadratic twists for elliptic curve 1638p1

-4	8	-3	5	-7	13
13104ch1	52416bm1	546a1	40950bj1	11466bv1	21294bf1

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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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