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	15730k	Isogeny class
Conductor	15730	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	11520	Modular degree for the optimal curve
Δ	29478775040 = 28 · 5 · 116 · 13	Discriminant
Eigenvalues	2+  0 5-  0 11- 13+ -2  8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-809,3405]	[a1,a2,a3,a4,a6]
Generators	[114:1119:1]	Generators of the group modulo torsion
j	33076161/16640	j-invariant
L	3.5809710895629	L(r)(E,1)/r!
Ω	1.0420781519489	Real period
R	3.4363747890366	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	125840cd1 78650cd1 130b1	Quadratic twists by: -4 5 -11

Hecke Eigenvalues for elliptic curve 15730k1

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	-	0	-	+	-2	8	-4	2	-4	6	-10	0	8	6	8	2	4	-12	-10	8	-12	10	-14

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Quadratic twists for elliptic curve 15730k1

-4	5	-11
125840cd1	78650cd1	130b1

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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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