Cremona's table of elliptic curves

6601 = 7 · 23 · 41

Field	Data	Notes
Atkin-Lehner	7+ 23+ 41-	Signs for the Atkin-Lehner involutions
Class	6601a	Isogeny class
Conductor	6601	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	992	Modular degree for the optimal curve
Δ	1062761 = 72 · 232 · 41	Discriminant
Eigenvalues	1 -2  2 7+  4  2  4  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-50,-129]	[a1,a2,a3,a4,a6]
j	13430356633/1062761	j-invariant
L	1.8087409742021	L(r)(E,1)/r!
Ω	1.8087409742021	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	105616y1 59409d1 46207c1	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 6601a1

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
1	-2	2	+	4	2	4	4	+	-2	8	-6	-	-12	-6	0	0	-2	-8	6	6	16	-12	12	4

---

Quadratic twists for elliptic curve 6601a1

-4	-3	-7
105616y1	59409d1	46207c1

---

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
Back to Tables and computations