Cremona's table of elliptic curves

1710 = 2 · 3² · 5 · 19

Field	Data	Notes
Atkin-Lehner	2- 3+ 5- 19+	Signs for the Atkin-Lehner involutions
Class	1710m	Isogeny class
Conductor	1710	Conductor
∏ cp	80	Product of Tamagawa factors cp
Δ	194940000 = 25 · 33 · 54 · 192	Discriminant
Eigenvalues	2- 3+ 5- -4 -6  0  4 19+	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-542,4941]	[a1,a2,a3,a4,a6]
Generators	[-9:99:1]	Generators of the group modulo torsion
j	651038076963/7220000	j-invariant
L	3.8887348431364	L(r)(E,1)/r!
Ω	1.7968941740057	Real period
R	0.10820711924475	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	13680y2 54720g2 1710a2 8550b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1710m2

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

---

Quadratic twists for elliptic curve 1710m2

-4	8	-3	5	-7	-19
13680y2	54720g2	1710a2	8550b2	83790cz2	32490g2

---

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