Cremona's table of elliptic curves

1575 = 3² · 5² · 7

Field	Data	Notes
Atkin-Lehner	3- 5- 7-	Signs for the Atkin-Lehner involutions
Class	1575j	Isogeny class
Conductor	1575	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	1920	Modular degree for the optimal curve
Δ	269103515625 = 39 · 59 · 7	Discriminant
Eigenvalues	-1 3- 5- 7-  6  2  4 -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-4055,-95178]	[a1,a2,a3,a4,a6]
j	5177717/189	j-invariant
L	1.1992622118901	L(r)(E,1)/r!
Ω	0.59963110594507	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	25200fi1 100800in1 525c1 1575h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1575j1

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	-	-	-	6	2	4	-6	0	2	-10	4	-2	4	0	6	8	-2	16	-10	6	4	8	-6	2

---

Quadratic twists for elliptic curve 1575j1

-4	8	-3	5	-7
25200fi1	100800in1	525c1	1575h1	11025bn1

---

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