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	13680bo	Isogeny class
Conductor	13680	Conductor
∏ cp	144	Product of Tamagawa factors cp
Δ	1.125047475E+25	Discriminant
Eigenvalues	2- 3- 5- -2  6 -4  6 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-66705267,133900237874]	[a1,a2,a3,a4,a6]
j	10993009831928446009969/3767761230468750000	j-invariant
L	2.3760042070606	L(r)(E,1)/r!
Ω	0.066000116862795	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	1710j4 54720ed4 4560n4 68400ej4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13680bo4

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

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Quadratic twists for elliptic curve 13680bo4

-4	8	-3	5
1710j4	54720ed4	4560n4	68400ej4

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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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