Cremona's table of elliptic curves

13456 = 2⁴ · 29²

Field	Data	Notes
Atkin-Lehner	2- 29-	Signs for the Atkin-Lehner involutions
Class	13456o	Isogeny class
Conductor	13456	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	69600	Modular degree for the optimal curve
Δ	4098018614976512 = 213 · 298	Discriminant
Eigenvalues	2-  2  0  1  6 -4 -3  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-40648,-667536]	[a1,a2,a3,a4,a6]
Generators	[-5037:16820:27]	Generators of the group modulo torsion
j	3625/2	j-invariant
L	7.0879990844437	L(r)(E,1)/r!
Ω	0.35985359069589	Real period
R	3.2828161543592	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	1682d1 53824bo1 121104cl1 13456i1	Quadratic twists by: -4 8 -3 29

Hecke Eigenvalues for elliptic curve 13456o1

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 13456o1

-4	8	-3	29
1682d1	53824bo1	121104cl1	13456i1

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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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