Cremona's table of elliptic curves

115520 = 2⁶ · 5 · 19²

Field	Data	Notes
Atkin-Lehner	2+ 5+ 19+	Signs for the Atkin-Lehner involutions
Class	115520f	Isogeny class
Conductor	115520	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	583680	Modular degree for the optimal curve
Δ	-8260805063142400 = -1 · 210 · 52 · 199	Discriminant
Eigenvalues	2+  2 5+  0  4  2 -2 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-36581,-5123419]	[a1,a2,a3,a4,a6]
Generators	[317088412308315344941:5751430619577753690180:721157522045959081]	Generators of the group modulo torsion
j	-16384/25	j-invariant
L	10.564633757631	L(r)(E,1)/r!
Ω	0.16376059952316	Real period
R	32.256335836175	Regulator
r	1	Rank of the group of rational points
S	0.99999999694511	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	115520bq1 7220g1 115520h1	Quadratic twists by: -4 8 -19

Hecke Eigenvalues for elliptic curve 115520f1

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

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Quadratic twists for elliptic curve 115520f1

-4	8	-19
115520bq1	7220g1	115520h1

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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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