Cremona's table of elliptic curves

123840 = 2⁶ · 3² · 5 · 43

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 43-	Signs for the Atkin-Lehner involutions
Class	123840fm	Isogeny class
Conductor	123840	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	46080	Modular degree for the optimal curve
Δ	-50155200 = -1 · 26 · 36 · 52 · 43	Discriminant
Eigenvalues	2- 3- 5+ -2 -5 -1  1 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1398,20122]	[a1,a2,a3,a4,a6]
Generators	[-43:27:1] [21:5:1]	Generators of the group modulo torsion
j	-6476460544/1075	j-invariant
L	10.155905763688	L(r)(E,1)/r!
Ω	1.9399156876145	Real period
R	1.308807623354	Regulator
r	2	Rank of the group of rational points
S	1.0000000001214	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	123840ep1 61920v1 13760u1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 123840fm1

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	-5	-1	1	-2	-1	-6	7	2	-5	-	-12	9	0	-12	-3	-8	-4	8	9	-2	-3

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Quadratic twists for elliptic curve 123840fm1

-4	8	-3
123840ep1	61920v1	13760u1

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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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