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	2046b	Isogeny class
Conductor	2046	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	7040	Modular degree for the optimal curve
Δ	1917563839488 = 210 · 311 · 11 · 312	Discriminant
Eigenvalues	2+ 3+  0  4 11- -2 -2 -6	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-40265,3092421]	[a1,a2,a3,a4,a6]
Generators	[82:551:1]	Generators of the group modulo torsion
j	7219775199978393625/1917563839488	j-invariant
L	2.1682857201599	L(r)(E,1)/r!
Ω	0.81217602709531	Real period
R	2.66972386259	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	16368s1 65472r1 6138l1 51150cq1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2046b1

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	4	-	-2	-2	-6	-6	-2	-	2	-6	4	-12	6	-10	10	8	0	-4	-6	-12	0	2

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Quadratic twists for elliptic curve 2046b1

-4	8	-3	5	-7	-11	-31
16368s1	65472r1	6138l1	51150cq1	100254w1	22506ba1	63426j1

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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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