Cremona's table of elliptic curves

660 = 2² · 3 · 5 · 11

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 11+	Signs for the Atkin-Lehner involutions
Class	660c	Isogeny class
Conductor	660	Conductor
∏ cp	36	Product of Tamagawa factors cp
deg	144	Modular degree for the optimal curve
Δ	-3207600 = -1 · 24 · 36 · 52 · 11	Discriminant
Eigenvalues	2- 3- 5+ -4 11+ -4 -6  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-41,120]	[a1,a2,a3,a4,a6]
Generators	[-5:15:1]	Generators of the group modulo torsion
j	-488095744/200475	j-invariant
L	2.2071066960177	L(r)(E,1)/r!
Ω	2.363154292465	Real period
R	0.93396639527736	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	2640p1 10560n1 1980f1 3300c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 660c1

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
-	-	+	-4	+	-4	-6	2	0	0	-4	-10	0	-4	12	6	12	-10	-4	0	8	-10	-6	-6	-10

---

Quadratic twists for elliptic curve 660c1

-4	8	-3	5	-7	-11	13
2640p1	10560n1	1980f1	3300c1	32340p1	7260p1	111540bo1

---

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