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	13754d	Isogeny class
Conductor	13754	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	-2601878785064 = -1 · 23 · 133 · 236	Discriminant
Eigenvalues	2+  1  3  1 -6 13-  3 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-2392,89518]	[a1,a2,a3,a4,a6]
Generators	[44:242:1]	Generators of the group modulo torsion
j	-10218313/17576	j-invariant
L	4.8807971488524	L(r)(E,1)/r!
Ω	0.72549326775102	Real period
R	1.1212594625407	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	110032q2 123786bp2 26a1	Quadratic twists by: -4 -3 -23

Hecke Eigenvalues for elliptic curve 13754d2

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	3	1	-6	-	3	-2	-	6	-4	7	0	1	3	0	-6	-8	-14	-3	2	-8	-12	6	10

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Quadratic twists for elliptic curve 13754d2

-4	-3	-23
110032q2	123786bp2	26a1

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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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