Cremona's table of elliptic curves

13754 = 2 · 13 · 23²

Field	Data	Notes
Atkin-Lehner	2- 13+ 23-	Signs for the Atkin-Lehner involutions
Class	13754h	Isogeny class
Conductor	13754	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1152	Modular degree for the optimal curve
Δ	-110032 = -1 · 24 · 13 · 232	Discriminant
Eigenvalues	2-  2  0  0  1 13+  1 -5	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,12,5]	[a1,a2,a3,a4,a6]
Generators	[3:7:1]	Generators of the group modulo torsion
j	359375/208	j-invariant
L	9.8673279444109	L(r)(E,1)/r!
Ω	1.9962496247551	Real period
R	1.2357332246989	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	110032n1 123786f1 13754i1	Quadratic twists by: -4 -3 -23

Hecke Eigenvalues for elliptic curve 13754h1

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
-	2	0	0	1	+	1	-5	-	-9	-7	6	-2	-2	-9	-1	-3	10	-5	0	6	10	-12	8	-12

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Quadratic twists for elliptic curve 13754h1

-4	-3	-23
110032n1	123786f1	13754i1

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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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