Cremona's table of elliptic curves

15870 = 2 · 3 · 5 · 23²

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5- 23-	Signs for the Atkin-Lehner involutions
Class	15870g	Isogeny class
Conductor	15870	Conductor
∏ cp	64	Product of Tamagawa factors cp
deg	236544	Modular degree for the optimal curve
Δ	-313788713195520000 = -1 · 214 · 32 · 54 · 237	Discriminant
Eigenvalues	2+ 3+ 5-  2 -6 -2  0  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,90713,24852661]	[a1,a2,a3,a4,a6]
Generators	[427:11689:1]	Generators of the group modulo torsion
j	557644990391/2119680000	j-invariant
L	3.1060344751804	L(r)(E,1)/r!
Ω	0.2176827687865	Real period
R	0.89178925728003	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	126960dd1 47610bv1 79350di1 690a1	Quadratic twists by: -4 -3 5 -23

Hecke Eigenvalues for elliptic curve 15870g1

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

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Quadratic twists for elliptic curve 15870g1

-4	-3	5	-23
126960dd1	47610bv1	79350di1	690a1

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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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