Cremona's table of elliptic curves

15376 = 2⁴ · 31²

Field	Data	Notes
Atkin-Lehner	2+ 31+	Signs for the Atkin-Lehner involutions
Class	15376b	Isogeny class
Conductor	15376	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	89280	Modular degree for the optimal curve
Δ	873360422339584 = 210 · 318	Discriminant
Eigenvalues	2+  1 -3 -5 -1  1 -5  5	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-69512,-6932476]	[a1,a2,a3,a4,a6]
Generators	[320:1922:1]	Generators of the group modulo torsion
j	42532	j-invariant
L	3.126630332153	L(r)(E,1)/r!
Ω	0.29444628283268	Real period
R	0.88488985214148	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	7688f1 61504bh1 15376j1	Quadratic twists by: -4 8 -31

Hecke Eigenvalues for elliptic curve 15376b1

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
+	1	-3	-5	-1	1	-5	5	4	2	+	5	-9	5	0	9	-7	14	7	1	15	7	15	-18	-10

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Quadratic twists for elliptic curve 15376b1

-4	8	-31
7688f1	61504bh1	15376j1

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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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