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	13680l	Isogeny class
Conductor	13680	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	2918523156480 = 211 · 37 · 5 · 194	Discriminant
Eigenvalues	2+ 3- 5+  0  4  2 -6 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-6843,-201782]	[a1,a2,a3,a4,a6]
Generators	[-39:76:1]	Generators of the group modulo torsion
j	23735908082/1954815	j-invariant
L	4.6868694355001	L(r)(E,1)/r!
Ω	0.52766161193047	Real period
R	0.5551462018377	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	6840m4 54720ei3 4560j4 68400bw3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13680l3

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

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Quadratic twists for elliptic curve 13680l3

-4	8	-3	5
6840m4	54720ei3	4560j4	68400bw3

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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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