Cremona's table of elliptic curves

13680 = 2⁴ · 3² · 5 · 19

Field	Data	Notes
Atkin-Lehner	2- 3- 5- 19-	Signs for the Atkin-Lehner involutions
Class	13680bt	Isogeny class
Conductor	13680	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	3072	Modular degree for the optimal curve
Δ	189481680 = 24 · 38 · 5 · 192	Discriminant
Eigenvalues	2- 3- 5-  2  0 -4  2 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-192,-781]	[a1,a2,a3,a4,a6]
Generators	[615:2204:27]	Generators of the group modulo torsion
j	67108864/16245	j-invariant
L	5.4009689151724	L(r)(E,1)/r!
Ω	1.3051459170074	Real period
R	4.1382107891481	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	3420b1 54720dl1 4560p1 68400fj1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13680bt1

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	-4	2	-	-6	2	0	-4	-2	-2	-6	12	-4	6	-12	0	-2	0	-6	14	8

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Quadratic twists for elliptic curve 13680bt1

-4	8	-3	5
3420b1	54720dl1	4560p1	68400fj1

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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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