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	13680bh	Isogeny class
Conductor	13680	Conductor
∏ cp	128	Product of Tamagawa factors cp
Δ	1459261578240000 = 213 · 37 · 54 · 194	Discriminant
Eigenvalues	2- 3- 5+ -4 -4 -2  2 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-31683,1154882]	[a1,a2,a3,a4,a6]
Generators	[-137:1710:1] [-119:1800:1]	Generators of the group modulo torsion
j	1177918188481/488703750	j-invariant
L	5.8041335616598	L(r)(E,1)/r!
Ω	0.43315664816991	Real period
R	0.41873805831731	Regulator
r	2	Rank of the group of rational points
S	0.99999999999982	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1710d4 54720eq3 4560u4 68400fs3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13680bh3

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	-4	-2	2	-	-8	-6	-4	-10	2	-12	0	-6	0	-10	4	-8	2	12	-8	-6	18

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Quadratic twists for elliptic curve 13680bh3

-4	8	-3	5
1710d4	54720eq3	4560u4	68400fs3

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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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