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	6720bs	Isogeny class
Conductor	6720	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	-141120 = -1 · 26 · 32 · 5 · 72	Discriminant
Eigenvalues	2- 3+ 5- 7- -2  0 -6  6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,0,-18]	[a1,a2,a3,a4,a6]
j	-64/2205	j-invariant
L	1.4917508081962	L(r)(E,1)/r!
Ω	1.4917508081962	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	6720ch1 3360j2 20160ec1 33600gd1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6720bs1

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

---

Quadratic twists for elliptic curve 6720bs1

-4	8	-3	5	-7
6720ch1	3360j2	20160ec1	33600gd1	47040fz1

---

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