Cremona's table of elliptic curves

13456 = 2⁴ · 29²

Field	Data	Notes
Atkin-Lehner	2- 29-	Signs for the Atkin-Lehner involutions
Class	13456n	Isogeny class
Conductor	13456	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-104749957382144 = -1 · 232 · 293	Discriminant
Eigenvalues	2- -1 -1  2  5  1 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,5984,-461056]	[a1,a2,a3,a4,a6]
Generators	[242:3886:1]	Generators of the group modulo torsion
j	237176659/1048576	j-invariant
L	3.9872843455799	L(r)(E,1)/r!
Ω	0.30106087559319	Real period
R	3.3110283241916	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	1682i2 53824bj2 121104cp2 13456m2	Quadratic twists by: -4 8 -3 29

Hecke Eigenvalues for elliptic curve 13456n2

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	-1	2	5	1	-2	-4	6	-	-5	-8	10	9	3	-1	-10	-10	8	-8	-16	1	-14	14	2

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Quadratic twists for elliptic curve 13456n2

-4	8	-3	29
1682i2	53824bj2	121104cp2	13456m2

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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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