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	15730ba	Isogeny class
Conductor	15730	Conductor
∏ cp	2128	Product of Tamagawa factors cp
deg	6128640	Modular degree for the optimal curve
Δ	-6.5111179469129E+26	Discriminant
Eigenvalues	2- -1 5- -1 11- 13-  1 -3	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-129448525,1352188669635]	[a1,a2,a3,a4,a6]
Generators	[12183:1252308:1]	Generators of the group modulo torsion
j	-135412551115258010417641/367535633653760000000	j-invariant
L	6.2394213333285	L(r)(E,1)/r!
Ω	0.045152094140222	Real period
R	0.064937384479559	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	125840co1 78650c1 1430b1	Quadratic twists by: -4 5 -11

Hecke Eigenvalues for elliptic curve 15730ba1

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
-	-1	-	-1	-	-	1	-3	6	1	-7	7	-6	-4	6	-5	-14	-13	8	-5	-10	-2	14	17	8

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Quadratic twists for elliptic curve 15730ba1

-4	5	-11
125840co1	78650c1	1430b1

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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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