Cremona's table of elliptic curves

15730 = 2 · 5 · 11² · 13

Field	Data	Notes
Atkin-Lehner	2+ 5+ 11- 13-	Signs for the Atkin-Lehner involutions
Class	15730i	Isogeny class
Conductor	15730	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	112000	Modular degree for the optimal curve
Δ	18424234400000 = 28 · 55 · 116 · 13	Discriminant
Eigenvalues	2+  2 5+  4 11- 13- -2 -6	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-101763,12450893]	[a1,a2,a3,a4,a6]
Generators	[45282:1801111:27]	Generators of the group modulo torsion
j	65787589563409/10400000	j-invariant
L	5.4659570484927	L(r)(E,1)/r!
Ω	0.66622057540821	Real period
R	8.2044254564542	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	125840ca1 78650by1 130c1	Quadratic twists by: -4 5 -11

Hecke Eigenvalues for elliptic curve 15730i1

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	+	4	-	-	-2	-6	6	-2	-6	-2	-10	10	-12	2	10	-2	-12	10	-10	4	0	-14	14

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Quadratic twists for elliptic curve 15730i1

-4	5	-11
125840ca1	78650by1	130c1

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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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