Cremona's table of elliptic curves

3570 = 2 · 3 · 5 · 7 · 17

Field	Data	Notes
Atkin-Lehner	2+ 3- 5- 7- 17-	Signs for the Atkin-Lehner involutions
Class	3570p	Isogeny class
Conductor	3570	Conductor
∏ cp	320	Product of Tamagawa factors cp
Δ	1546622367494400 = 28 · 310 · 52 · 72 · 174	Discriminant
Eigenvalues	2+ 3- 5- 7-  0 -6 17-  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-52573,4231928]	[a1,a2,a3,a4,a6]
Generators	[-173:2942:1]	Generators of the group modulo torsion
j	16069416876629693641/1546622367494400	j-invariant
L	3.3064654916508	L(r)(E,1)/r!
Ω	0.46310312776186	Real period
R	0.35699019218794	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	28560cu2 114240bc2 10710bb2 17850bc2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3570p2

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
+	-	-	-	0	-6	-	0	-8	-10	4	-2	10	-12	-8	-6	4	-10	4	-12	6	-8	12	-6	6

---

Quadratic twists for elliptic curve 3570p2

-4	8	-3	5	-7	17
28560cu2	114240bc2	10710bb2	17850bc2	24990a2	60690c2

---

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