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	-25543473228 = -1 · 22 · 33 · 72 · 136	Discriminant
Eigenvalues	2+ 3+  0 7-  0 13- -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-897,13113]	[a1,a2,a3,a4,a6]
Generators	[-32:107:1]	Generators of the group modulo torsion
j	-2958077788875/946054564	j-invariant
L	2.205037763062	L(r)(E,1)/r!
Ω	1.1267576324185	Real period
R	1.4677320789447	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	13104bg2 52416p2 1638m4 40950cw2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1638c2

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 1638c2

-4	8	-3	5	-7	13
13104bg2	52416p2	1638m4	40950cw2	11466b2	21294bm2

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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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