Cremona's table of elliptic curves

4004 = 2² · 7 · 11 · 13

Field	Data	Notes
Atkin-Lehner	2- 7- 11+ 13-	Signs for the Atkin-Lehner involutions
Class	4004b	Isogeny class
Conductor	4004	Conductor
∏ cp	18	Product of Tamagawa factors cp
deg	1368	Modular degree for the optimal curve
Δ	10202192 = 24 · 73 · 11 · 132	Discriminant
Eigenvalues	2- -2  0 7- 11+ 13-  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1253,16660]	[a1,a2,a3,a4,a6]
j	13608288256000/637637	j-invariant
L	1.0775747483415	L(r)(E,1)/r!
Ω	2.1551494966831	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	16016i1 64064q1 36036n1 100100a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4004b1

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	0	-	+	-	6	-4	0	6	-4	2	-6	2	0	6	0	-10	-4	0	14	-10	12	0	-4

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Quadratic twists for elliptic curve 4004b1

-4	8	-3	5	-7	-11	13
16016i1	64064q1	36036n1	100100a1	28028e1	44044c1	52052c1

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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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