Cremona's table of elliptic curves

15576 = 2³ · 3 · 11 · 59

Field	Data	Notes
Atkin-Lehner	2- 3+ 11- 59+	Signs for the Atkin-Lehner involutions
Class	15576g	Isogeny class
Conductor	15576	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	29952	Modular degree for the optimal curve
Δ	197379072 = 210 · 33 · 112 · 59	Discriminant
Eigenvalues	2- 3+  0 -4 11- -4 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-64248,-6246756]	[a1,a2,a3,a4,a6]
Generators	[540300:3513961:1728]	Generators of the group modulo torsion
j	28642396591574500/192753	j-invariant
L	2.9684877245719	L(r)(E,1)/r!
Ω	0.29987073789115	Real period
R	9.8992243973117	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	31152h1 124608be1 46728d1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 15576g1

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	-4	-	-4	-2	-4	0	4	-2	4	6	12	8	-4	+	8	16	10	-6	12	4	-10	6

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Quadratic twists for elliptic curve 15576g1

-4	8	-3
31152h1	124608be1	46728d1

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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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