Cremona's table of elliptic curves

2124 = 2² · 3² · 59

Field	Data	Notes
Atkin-Lehner	2- 3- 59+	Signs for the Atkin-Lehner involutions
Class	2124a	Isogeny class
Conductor	2124	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	180	Modular degree for the optimal curve
Δ	-688176 = -1 · 24 · 36 · 59	Discriminant
Eigenvalues	2- 3-  1 -3  2  0 -2 -5	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-12,-43]	[a1,a2,a3,a4,a6]
Generators	[11:34:1]	Generators of the group modulo torsion
j	-16384/59	j-invariant
L	3.0628608389699	L(r)(E,1)/r!
Ω	1.1760151320915	Real period
R	2.6044399900899	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	8496u1 33984v1 236a1 53100i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2124a1

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	-3	2	0	-2	-5	4	-5	-4	8	1	0	-8	-3	+	-2	-14	0	-2	-13	-4	18	2

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Quadratic twists for elliptic curve 2124a1

-4	8	-3	5	-7	-59
8496u1	33984v1	236a1	53100i1	104076t1	125316d1

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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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