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	1725o	Isogeny class
Conductor	1725	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	2880	Modular degree for the optimal curve
Δ	1995692175 = 38 · 52 · 233	Discriminant
Eigenvalues	1 3- 5+ -3  5 -1 -8  1	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-15261,724333]	[a1,a2,a3,a4,a6]
Generators	[23:609:1]	Generators of the group modulo torsion
j	15721420060947505/79827687	j-invariant
L	3.8407268271597	L(r)(E,1)/r!
Ω	1.3056441386108	Real period
R	0.12256807175289	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	27600bm1 110400bl1 5175d1 1725j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1725o1

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	-	+	-3	5	-1	-8	1	-	-5	-6	-8	-5	-13	-2	10	-4	4	0	10	-13	-9	15	-6	-2

---

Quadratic twists for elliptic curve 1725o1

-4	8	-3	5	-7	-23
27600bm1	110400bl1	5175d1	1725j1	84525s1	39675bd1

---

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