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	13680bi	Isogeny class
Conductor	13680	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	18432	Modular degree for the optimal curve
Δ	42633378000 = 24 · 310 · 53 · 192	Discriminant
Eigenvalues	2- 3- 5-  2  4  0  2 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-30432,2043331]	[a1,a2,a3,a4,a6]
j	267219216891904/3655125	j-invariant
L	3.125112926122	L(r)(E,1)/r!
Ω	1.0417043087073	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	3420e1 54720dx1 4560v1 68400em1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13680bi1

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	4	0	2	+	-2	6	0	-8	2	6	-2	4	4	-10	12	8	-2	8	14	2	-4

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Quadratic twists for elliptic curve 13680bi1

-4	8	-3	5
3420e1	54720dx1	4560v1	68400em1

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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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