Cremona's table of elliptic curves

15675 = 3 · 5² · 11 · 19

Field	Data	Notes
Atkin-Lehner	3+ 5- 11- 19+	Signs for the Atkin-Lehner involutions
Class	15675o	Isogeny class
Conductor	15675	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	18000	Modular degree for the optimal curve
Δ	-51069541875 = -1 · 3 · 54 · 11 · 195	Discriminant
Eigenvalues	2 3+ 5-  2 11-  6 -3 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,242,-10857]	[a1,a2,a3,a4,a6]
Generators	[1386:18241:8]	Generators of the group modulo torsion
j	2497433600/81711267	j-invariant
L	9.0160089325875	L(r)(E,1)/r!
Ω	0.54219056050382	Real period
R	5.54295210907	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	47025bi1 15675t2	Quadratic twists by: -3 5

Hecke Eigenvalues for elliptic curve 15675o1

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	+	-	2	-	6	-3	+	-4	0	-8	-8	2	-4	2	1	5	-8	-8	-3	6	0	-9	-10	2

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Quadratic twists for elliptic curve 15675o1

-3	5
47025bi1	15675t2

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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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