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
Conductor	4004	Conductor
Count	4	Number of curves in isogeny class
Curves	4004b1 4004b2 4004b3 4004b4	Curves in isogeny class
deg	1368	Modular degree for the optimal curve
Eigenvalues	2- -2  0 7- 11+ 13-  6 -4	Hecke eigenvalues for primes less than 20
L	1.0775747483415	L(r)(E,1)/r!
r	0	Rank of the group of rational points
Twists	16016i 64064q 36036n 100100a	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for isogeny class 4004b

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 isogeny class 4004b

-4	8	-3	5	-7	-11	13
16016i	64064q	36036n	100100a	28028e	44044c	52052c

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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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