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	13680r	Isogeny class
Conductor	13680	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	5263380000000 = 28 · 36 · 57 · 192	Discriminant
Eigenvalues	2+ 3- 5+ -4  4 -4  2 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-3749943,-2795021242]	[a1,a2,a3,a4,a6]
Generators	[-58159631501939:-70153198308:52020433837]	Generators of the group modulo torsion
j	31248575021659890256/28203125	j-invariant
L	3.7383821534336	L(r)(E,1)/r!
Ω	0.10849091902122	Real period
R	17.229009520615	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	6840q2 54720es2 1520c2 68400cg2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13680r2

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	-4	2	-	0	-2	-8	4	-6	0	12	8	0	2	14	8	6	4	4	-14	-12

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Quadratic twists for elliptic curve 13680r2

-4	8	-3	5
6840q2	54720es2	1520c2	68400cg2

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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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