Cremona's table of elliptic curves

2046 = 2 · 3 · 11 · 31

Field	Data	Notes
Atkin-Lehner	2+ 3+ 11+ 31+	Signs for the Atkin-Lehner involutions
Class	2046a	Isogeny class
Conductor	2046	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	288	Modular degree for the optimal curve
Δ	-220968 = -1 · 23 · 34 · 11 · 31	Discriminant
Eigenvalues	2+ 3+ -2  3 11+  4 -7 -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,4,24]	[a1,a2,a3,a4,a6]
Generators	[-1:5:1]	Generators of the group modulo torsion
j	4657463/220968	j-invariant
L	1.8846421864553	L(r)(E,1)/r!
Ω	2.3900263944429	Real period
R	0.39427225382055	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	16368bb1 65472z1 6138o1 51150cg1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2046a1

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	3	+	4	-7	-2	-3	0	+	7	10	1	8	-6	5	-10	-5	-6	-6	-10	9	-2	-7

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Quadratic twists for elliptic curve 2046a1

-4	8	-3	5	-7	-11	-31
16368bb1	65472z1	6138o1	51150cg1	100254v1	22506y1	63426q1

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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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