Cremona's table of elliptic curves

2001 = 3 · 23 · 29

Field	Data	Notes
Atkin-Lehner	3+ 23- 29+	Signs for the Atkin-Lehner involutions
Class	2001b	Isogeny class
Conductor	2001	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	5760	Modular degree for the optimal curve
Δ	-3095193917547 = -1 · 38 · 23 · 295	Discriminant
Eigenvalues	0 3+  4 -4  4 -5 -5  5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,689,84129]	[a1,a2,a3,a4,a6]
j	36120262639616/3095193917547	j-invariant
L	1.2232212468355	L(r)(E,1)/r!
Ω	0.61161062341774	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	32016bc1 128064bs1 6003b1 50025l1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2001b1

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	-4	4	-5	-5	5	-	+	-2	5	-2	1	6	2	9	-10	8	-3	8	13	-6	-9	-6

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Quadratic twists for elliptic curve 2001b1

-4	8	-3	5	-7	-23	29
32016bc1	128064bs1	6003b1	50025l1	98049s1	46023a1	58029g1

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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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