Cremona's table of elliptic curves

13456 = 2⁴ · 29²

Field	Data	Notes
Atkin-Lehner	2- 29+	Signs for the Atkin-Lehner involutions
Class	13456i	Isogeny class
Conductor	13456	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	2400	Modular degree for the optimal curve
Δ	6889472 = 213 · 292	Discriminant
Eigenvalues	2- -2  0  1 -6 -4  3 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-48,-44]	[a1,a2,a3,a4,a6]
Generators	[-6:8:1] [-4:10:1]	Generators of the group modulo torsion
j	3625/2	j-invariant
L	4.8745411474222	L(r)(E,1)/r!
Ω	1.9378708923365	Real period
R	0.62885267108065	Regulator
r	2	Rank of the group of rational points
S	1.0000000000003	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	1682f1 53824z1 121104bp1 13456o1	Quadratic twists by: -4 8 -3 29

Hecke Eigenvalues for elliptic curve 13456i1

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	0	1	-6	-4	3	-4	-9	+	5	-2	6	-4	-9	-12	-6	-2	-8	-3	-11	11	0	-3	-17

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Quadratic twists for elliptic curve 13456i1

-4	8	-3	29
1682f1	53824z1	121104bp1	13456o1

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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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