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	1710a	Isogeny class
Conductor	1710	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	142111260000 = 25 · 39 · 54 · 192	Discriminant
Eigenvalues	2+ 3+ 5+ -4  6  0 -4 19+	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-4875,-128539]	[a1,a2,a3,a4,a6]
Generators	[-37:31:1]	Generators of the group modulo torsion
j	651038076963/7220000	j-invariant
L	1.9530226635715	L(r)(E,1)/r!
Ω	0.57173233269592	Real period
R	1.7079868951633	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	13680w2 54720n2 1710m2 8550t2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1710a2

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 1710a2

-4	8	-3	5	-7	-19
13680w2	54720n2	1710m2	8550t2	83790t2	32490bd2

---

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