Cremona's table of elliptic curves

14560 = 2⁵ · 5 · 7 · 13

Field	Data	Notes
Atkin-Lehner	2+ 5- 7+ 13-	Signs for the Atkin-Lehner involutions
Class	14560f	Isogeny class
Conductor	14560	Conductor
∏ cp	36	Product of Tamagawa factors cp
deg	82944	Modular degree for the optimal curve
Δ	42199976000 = 26 · 53 · 74 · 133	Discriminant
Eigenvalues	2+ -2 5- 7+  2 13- -2  6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-366150,85156000]	[a1,a2,a3,a4,a6]
Generators	[2890:-3185:8]	Generators of the group modulo torsion
j	84824642835624182464/659374625	j-invariant
L	3.5258716593094	L(r)(E,1)/r!
Ω	0.79015214309149	Real period
R	0.49580770124632	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	14560h1 29120bj2 72800br1 101920c1	Quadratic twists by: -4 8 5 -7

Hecke Eigenvalues for elliptic curve 14560f1

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	-	+	2	-	-2	6	2	2	-10	10	-10	-2	-8	-14	-14	10	4	-6	6	-4	-16	6	10

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Quadratic twists for elliptic curve 14560f1

-4	8	5	-7
14560h1	29120bj2	72800br1	101920c1

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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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