Cremona's table of elliptic curves

13456 = 2⁴ · 29²

Field	Data	Notes
Atkin-Lehner	2- 29+	Signs for the Atkin-Lehner involutions
Class	13456l	Isogeny class
Conductor	13456	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	80640	Modular degree for the optimal curve
Δ	-282621973446656 = -1 · 214 · 297	Discriminant
Eigenvalues	2- -3 -3  2 -1  3  4 -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-15979,-1121894]	[a1,a2,a3,a4,a6]
j	-185193/116	j-invariant
L	0.82582788441473	L(r)(E,1)/r!
Ω	0.20645697110368	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	1682g1 53824be1 121104cd1 464g1	Quadratic twists by: -4 8 -3 29

Hecke Eigenvalues for elliptic curve 13456l1

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	-3	2	-1	3	4	-8	0	+	3	8	2	7	11	1	4	-4	4	2	12	-7	0	6	6

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Quadratic twists for elliptic curve 13456l1

-4	8	-3	29
1682g1	53824be1	121104cd1	464g1

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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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