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	15730a	Isogeny class
Conductor	15730	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	51840	Modular degree for the optimal curve
Δ	-80306034737500 = -1 · 22 · 55 · 113 · 136	Discriminant
Eigenvalues	2+  0 5+  4 11+ 13+  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-15395,-848479]	[a1,a2,a3,a4,a6]
Generators	[77875:889127:343]	Generators of the group modulo torsion
j	-303180038976339/60335112500	j-invariant
L	3.5616462454672	L(r)(E,1)/r!
Ω	0.21202620009982	Real period
R	8.399071067138	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	125840bb1 78650bq1 15730r1	Quadratic twists by: -4 5 -11

Hecke Eigenvalues for elliptic curve 15730a1

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
+	0	+	4	+	+	2	-4	-2	-2	8	6	-2	-8	0	-4	-12	14	2	0	-6	-8	4	-2	16

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Quadratic twists for elliptic curve 15730a1

-4	5	-11
125840bb1	78650bq1	15730r1

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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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