Cremona's table of elliptic curves

15904 = 2⁵ · 7 · 71

Field	Data	Notes
Atkin-Lehner	2+ 7- 71-	Signs for the Atkin-Lehner involutions
Class	15904f	Isogeny class
Conductor	15904	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	3584	Modular degree for the optimal curve
Δ	-2035712 = -1 · 212 · 7 · 71	Discriminant
Eigenvalues	2+ -1  0 7- -3  1  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-593,5761]	[a1,a2,a3,a4,a6]
Generators	[15:4:1]	Generators of the group modulo torsion
j	-5639752000/497	j-invariant
L	3.8131086647548	L(r)(E,1)/r!
Ω	2.5009282347166	Real period
R	0.76233868125906	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	15904a1 31808z1 111328q1	Quadratic twists by: -4 8 -7

Hecke Eigenvalues for elliptic curve 15904f1

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	0	-	-3	1	6	-4	3	-1	0	-11	5	8	8	6	-12	-15	8	-	-4	14	9	0	-15

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Quadratic twists for elliptic curve 15904f1

-4	8	-7
15904a1	31808z1	111328q1

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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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