Cremona's table of elliptic curves

6720 = 2⁶ · 3 · 5 · 7

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5+ 7+	Signs for the Atkin-Lehner involutions
Class	6720c	Isogeny class
Conductor	6720	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	318637670400000000 = 222 · 34 · 58 · 74	Discriminant
Eigenvalues	2+ 3+ 5+ 7+  4  2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-483201,-126236799]	[a1,a2,a3,a4,a6]
Generators	[-955240:2664767:2197]	Generators of the group modulo torsion
j	47595748626367201/1215506250000	j-invariant
L	3.2776134934885	L(r)(E,1)/r!
Ω	0.18136104710698	Real period
R	9.0361561806463	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	6720cd4 210e3 20160ce4 33600da3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6720c3

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	2	2	-4	-8	2	0	-6	-6	4	0	10	-12	-14	12	-8	10	16	12	10	2

---

Quadratic twists for elliptic curve 6720c3

-4	8	-3	5	-7
6720cd4	210e3	20160ce4	33600da3	47040dm3

---

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