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	1710f	Isogeny class
Conductor	1710	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	39475350 = 2 · 37 · 52 · 192	Discriminant
Eigenvalues	2+ 3- 5+ -2  0  6 -8 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-270,1750]	[a1,a2,a3,a4,a6]
Generators	[5:20:1]	Generators of the group modulo torsion
j	2992209121/54150	j-invariant
L	2.0102900544216	L(r)(E,1)/r!
Ω	2.0462166023707	Real period
R	0.24561061278807	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	13680ba2 54720bu2 570h2 8550bc2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1710f2

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

---

Quadratic twists for elliptic curve 1710f2

-4	8	-3	5	-7	-19
13680ba2	54720bu2	570h2	8550bc2	83790bt2	32490bm2

---

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