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	13680m	Isogeny class
Conductor	13680	Conductor
∏ cp	128	Product of Tamagawa factors cp
Δ	197000313062400 = 210 · 310 · 52 · 194	Discriminant
Eigenvalues	2+ 3- 5+  0  4 -2 -2 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-389883,-93699718]	[a1,a2,a3,a4,a6]
Generators	[1177:32832:1]	Generators of the group modulo torsion
j	8780093172522724/263900025	j-invariant
L	4.5720343070502	L(r)(E,1)/r!
Ω	0.19105867567995	Real period
R	2.9912501295603	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	6840e4 54720eh4 4560d4 68400bv4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13680m3

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	-2	-	0	-6	0	6	6	-4	8	-6	-12	-2	-4	8	-6	-16	-4	6	10

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Quadratic twists for elliptic curve 13680m3

-4	8	-3	5
6840e4	54720eh4	4560d4	68400bv4

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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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