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	2046f	Isogeny class
Conductor	2046	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	640	Modular degree for the optimal curve
Δ	41100048 = 24 · 35 · 11 · 312	Discriminant
Eigenvalues	2- 3+  2  2 11+  4  2 -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-97,-241]	[a1,a2,a3,a4,a6]
j	100999381393/41100048	j-invariant
L	3.1524554459473	L(r)(E,1)/r!
Ω	1.5762277229736	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	16368z1 65472bc1 6138h1 51150u1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2046f1

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	2	+	4	2	-2	8	-6	+	-2	-10	8	6	4	10	4	-8	6	-4	-8	12	-4	-2

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Quadratic twists for elliptic curve 2046f1

-4	8	-3	5	-7	-11	-31
16368z1	65472bc1	6138h1	51150u1	100254cr1	22506d1	63426bg1

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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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