Cremona's table of elliptic curves

13456 = 2⁴ · 29²

Field	Data	Notes
Atkin-Lehner	2- 29-	Signs for the Atkin-Lehner involutions
Class	13456p	Isogeny class
Conductor	13456	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	208800	Modular degree for the optimal curve
Δ	65568297839624192 = 217 · 298	Discriminant
Eigenvalues	2- -2 -2  5  0  2 -7  6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-625984,190023732]	[a1,a2,a3,a4,a6]
Generators	[1962:80736:1]	Generators of the group modulo torsion
j	13239457/32	j-invariant
L	3.342043910715	L(r)(E,1)/r!
Ω	0.34936540119013	Real period
R	0.79717012124701	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	1682j1 53824bm1 121104ct1 13456h1	Quadratic twists by: -4 8 -3 29

Hecke Eigenvalues for elliptic curve 13456p1

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	-2	5	0	2	-7	6	-1	-	3	2	2	-10	-7	-2	12	-8	6	-11	7	-3	-4	-13	-11

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Quadratic twists for elliptic curve 13456p1

-4	8	-3	29
1682j1	53824bm1	121104ct1	13456h1

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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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