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	4004c	Isogeny class
Conductor	4004	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	-19731712 = -1 · 28 · 72 · 112 · 13	Discriminant
Eigenvalues	2-  2  4 7- 11- 13+  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,44,168]	[a1,a2,a3,a4,a6]
j	35969456/77077	j-invariant
L	4.5050946352328	L(r)(E,1)/r!
Ω	1.5016982117443	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	16016f2 64064o2 36036k2 100100f2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4004c2

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	4	-	-	+	2	4	8	-10	8	2	-10	-10	-12	-10	12	2	-4	0	2	10	-4	12	-8

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Quadratic twists for elliptic curve 4004c2

-4	8	-3	5	-7	-11	13
16016f2	64064o2	36036k2	100100f2	28028l2	44044i2	52052a2

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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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