Cremona's table of elliptic curves

1700 = 2² · 5² · 17

Field	Data	Notes
Atkin-Lehner	2- 5+ 17-	Signs for the Atkin-Lehner involutions
Class	1700b	Isogeny class
Conductor	1700	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	72	Modular degree for the optimal curve
Δ	-108800 = -1 · 28 · 52 · 17	Discriminant
Eigenvalues	2- -1 5+  1  0  1 17- -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,12,-8]	[a1,a2,a3,a4,a6]
Generators	[1:2:1]	Generators of the group modulo torsion
j	27440/17	j-invariant
L	2.4968828420112	L(r)(E,1)/r!
Ω	1.9283180907557	Real period
R	1.2948500841128	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	6800q1 27200t1 15300n1 1700c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1700b1

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
-	-1	+	1	0	1	-	-4	0	-6	-1	-2	0	-2	6	-3	-6	-10	4	-3	-2	-1	-12	-6	-8

---

Quadratic twists for elliptic curve 1700b1

-4	8	-3	5	-7	17
6800q1	27200t1	15300n1	1700c1	83300j1	28900c1

---

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