Cremona's table of elliptic curves

570 = 2 · 3 · 5 · 19

Field	Data	Notes
Atkin-Lehner	2- 3- 5- 19+	Signs for the Atkin-Lehner involutions
Class	570l	Isogeny class
Conductor	570	Conductor
∏ cp	1000	Product of Tamagawa factors cp
deg	2400	Modular degree for the optimal curve
Δ	-287450726400000 = -1 · 220 · 35 · 55 · 192	Discriminant
Eigenvalues	2- 3- 5- -2  2  4 -2 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,9335,-737383]	[a1,a2,a3,a4,a6]
j	89962967236397039/287450726400000	j-invariant
L	2.800031251919	L(r)(E,1)/r!
Ω	0.2800031251919	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	10	Number of elements in the torsion subgroup
Twists	4560s1 18240h1 1710c1 2850a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 570l1

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	2	4	-2	+	4	0	-8	8	-8	-6	-12	-6	0	2	8	-8	14	0	4	0	-12

---

Quadratic twists for elliptic curve 570l1

-4	8	-3	5	-7	-11	13	-19
4560s1	18240h1	1710c1	2850a1	27930cd1	68970bg1	96330bc1	10830g1

---

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