Cremona's table of elliptic curves

13456 = 2⁴ · 29²

Field	Data	Notes
Atkin-Lehner	2- 29-	Signs for the Atkin-Lehner involutions
Class	13456q	Isogeny class
Conductor	13456	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	39600	Modular degree for the optimal curve
Δ	-5933103054848 = -1 · 223 · 294	Discriminant
Eigenvalues	2- -3  0 -4  1  6  2 -1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,4205,-52142]	[a1,a2,a3,a4,a6]
Generators	[377:7424:1]	Generators of the group modulo torsion
j	2838375/2048	j-invariant
L	2.4401112078559	L(r)(E,1)/r!
Ω	0.42558875489289	Real period
R	0.47779129104536	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	1682e1 53824bq1 121104cn1 13456j1	Quadratic twists by: -4 8 -3 29

Hecke Eigenvalues for elliptic curve 13456q1

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
-	-3	0	-4	1	6	2	-1	6	-	0	-8	-11	-1	4	-2	4	-8	-8	2	6	4	-15	3	-3

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Quadratic twists for elliptic curve 13456q1

-4	8	-3	29
1682e1	53824bq1	121104cn1	13456j1

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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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