Cremona's table of elliptic curves

6630 = 2 · 3 · 5 · 13 · 17

Field	Data	Notes
Atkin-Lehner	2- 3+ 5- 13+ 17+	Signs for the Atkin-Lehner involutions
Class	6630q	Isogeny class
Conductor	6630	Conductor
∏ cp	160	Product of Tamagawa factors cp
deg	15360	Modular degree for the optimal curve
Δ	3666124800000 = 216 · 34 · 55 · 13 · 17	Discriminant
Eigenvalues	2- 3+ 5- -2  0 13+ 17+  2	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-13620,599157]	[a1,a2,a3,a4,a6]
Generators	[-3:801:1]	Generators of the group modulo torsion
j	279419703685750081/3666124800000	j-invariant
L	5.1790539690089	L(r)(E,1)/r!
Ω	0.79060110180678	Real period
R	0.16376950263455	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	53040cq1 19890e1 33150v1 86190a1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 6630q1

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	+	+	2	-8	6	-4	2	6	-2	0	-2	-14	-6	0	4	-6	10	-8	-10	2

---

Quadratic twists for elliptic curve 6630q1

-4	-3	5	13	17
53040cq1	19890e1	33150v1	86190a1	112710ck1

---

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