Cremona's table of elliptic curves

1725 = 3 · 5² · 23

Field	Data	Notes
Atkin-Lehner	3+ 5+ 23+	Signs for the Atkin-Lehner involutions
Class	1725b	Isogeny class
Conductor	1725	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	168	Modular degree for the optimal curve
Δ	-39675 = -1 · 3 · 52 · 232	Discriminant
Eigenvalues	0 3+ 5+ -3  2  3  0  1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-113,-427]	[a1,a2,a3,a4,a6]
Generators	[13:11:1]	Generators of the group modulo torsion
j	-6439567360/1587	j-invariant
L	1.999928169119	L(r)(E,1)/r!
Ω	0.7316000435381	Real period
R	1.3668179675381	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	27600cx1 110400df1 5175k1 1725t1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1725b1

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	+	+	-3	2	3	0	1	+	0	1	-6	4	5	-10	-4	-6	1	-7	-4	-2	0	-14	-2	-7

---

Quadratic twists for elliptic curve 1725b1

-4	8	-3	5	-7	-23
27600cx1	110400df1	5175k1	1725t1	84525bp1	39675b1

---

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