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	13680q	Isogeny class
Conductor	13680	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	-1459261578240 = -1 · 210 · 37 · 5 · 194	Discriminant
Eigenvalues	2+ 3- 5+ -4  0  2 -2 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,1797,-50182]	[a1,a2,a3,a4,a6]
Generators	[41:304:1]	Generators of the group modulo torsion
j	859687196/1954815	j-invariant
L	3.6674227602288	L(r)(E,1)/r!
Ω	0.44106132433135	Real period
R	1.0393743902247	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	6840f4 54720eo3 4560f4 68400cf3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13680q4

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

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Quadratic twists for elliptic curve 13680q4

-4	8	-3	5
6840f4	54720eo3	4560f4	68400cf3

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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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