Cremona's table of elliptic curves

3220 = 2² · 5 · 7 · 23

Field	Data	Notes
Atkin-Lehner	2- 5- 7+ 23+	Signs for the Atkin-Lehner involutions
Class	3220b	Isogeny class
Conductor	3220	Conductor
∏ cp	42	Product of Tamagawa factors cp
deg	5040	Modular degree for the optimal curve
Δ	-3628940000000 = -1 · 28 · 57 · 73 · 232	Discriminant
Eigenvalues	2- -1 5- 7+  5  1 -3 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,2995,65497]	[a1,a2,a3,a4,a6]
Generators	[99:-1150:1]	Generators of the group modulo torsion
j	11601902526464/14175546875	j-invariant
L	3.0250545210132	L(r)(E,1)/r!
Ω	0.5281587293077	Real period
R	0.13637019260778	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	12880z1 51520d1 28980b1 16100e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3220b1

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	-	+	5	1	-3	-4	+	-1	-10	-4	12	-6	11	-14	10	-6	8	-8	-10	-5	-4	6	1

---

Quadratic twists for elliptic curve 3220b1

-4	8	-3	5	-7	-23
12880z1	51520d1	28980b1	16100e1	22540e1	74060h1

---

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