Cremona's table of elliptic curves

23120 = 2⁴ · 5 · 17²

Field	Data	Notes
Atkin-Lehner	2+ 5+ 17+	Signs for the Atkin-Lehner involutions
Class	23120c	Isogeny class
Conductor	23120	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	10752	Modular degree for the optimal curve
Δ	-1257728000 = -1 · 211 · 53 · 173	Discriminant
Eigenvalues	2+ -1 5+  4 -2  1 17+ -5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-776,-8240]	[a1,a2,a3,a4,a6]
Generators	[74:578:1]	Generators of the group modulo torsion
j	-5142706/125	j-invariant
L	4.3135534684013	L(r)(E,1)/r!
Ω	0.45157892076994	Real period
R	2.3880396482229	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	11560b1 92480dx1 115600e1 23120j1	Quadratic twists by: -4 8 5 17

Hecke Eigenvalues for elliptic curve 23120c1

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	+	4	-2	1	+	-5	6	5	-3	-2	0	0	-13	3	7	-1	2	-3	1	-8	-10	-17	-17

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Quadratic twists for elliptic curve 23120c1

-4	8	5	17
11560b1	92480dx1	115600e1	23120j1

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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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