Cremona's table of elliptic curves

123786 = 2 · 3² · 13 · 23²

Field	Data	Notes
Atkin-Lehner	2+ 3- 13- 23-	Signs for the Atkin-Lehner involutions
Class	123786s	Isogeny class
Conductor	123786	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	221184	Modular degree for the optimal curve
Δ	-863416262592 = -1 · 26 · 38 · 132 · 233	Discriminant
Eigenvalues	2+ 3-  0 -2  4 13-  8  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-7137,-234563]	[a1,a2,a3,a4,a6]
j	-4533086375/97344	j-invariant
L	2.0750362900421	L(r)(E,1)/r!
Ω	0.25937951369807	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	41262u1 123786r1	Quadratic twists by: -3 -23

Hecke Eigenvalues for elliptic curve 123786s1

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	-2	4	-	8	0	-	10	0	-4	2	-10	8	6	8	-10	4	0	14	-4	-4	6	10

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Quadratic twists for elliptic curve 123786s1

-3	-23
41262u1	123786r1

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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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