Cremona's table of elliptic curves

15862 = 2 · 7 · 11 · 103

Field	Data	Notes
Atkin-Lehner	2+ 7- 11- 103+	Signs for the Atkin-Lehner involutions
Class	15862a	Isogeny class
Conductor	15862	Conductor
∏ cp	28	Product of Tamagawa factors cp
deg	143360	Modular degree for the optimal curve
Δ	-39741497135648 = -1 · 25 · 77 · 114 · 103	Discriminant
Eigenvalues	2+ -3 -2 7- 11-  1  4  8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-37198,2787316]	[a1,a2,a3,a4,a6]
Generators	[-21:1897:1]	Generators of the group modulo torsion
j	-5692316634680000697/39741497135648	j-invariant
L	2.1152232496894	L(r)(E,1)/r!
Ω	0.6495754762638	Real period
R	0.11629701281738	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	126896i1 111034e1	Quadratic twists by: -4 -7

Hecke Eigenvalues for elliptic curve 15862a1

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
+	-3	-2	-	-	1	4	8	0	8	10	2	-12	8	-8	-5	-12	1	-10	-5	2	-2	4	14	-10

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Quadratic twists for elliptic curve 15862a1

-4	-7
126896i1	111034e1

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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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