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	6	Product of Tamagawa factors cp
deg	840	Modular degree for the optimal curve
Δ	208208 = 24 · 7 · 11 · 132	Discriminant
Eigenvalues	2-  2  4 7- 11- 13+  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-21,38]	[a1,a2,a3,a4,a6]
j	67108864/13013	j-invariant
L	4.5050946352328	L(r)(E,1)/r!
Ω	3.0033964234885	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	16016f1 64064o1 36036k1 100100f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4004c1

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 4004c1

-4	8	-3	5	-7	-11	13
16016f1	64064o1	36036k1	100100f1	28028l1	44044i1	52052a1

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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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