Cremona's table of elliptic curves

2574 = 2 · 3² · 11 · 13

Field	Data	Notes
Atkin-Lehner	2+ 3- 11+ 13+	Signs for the Atkin-Lehner involutions
Class	2574g	Isogeny class
Conductor	2574	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	1280	Modular degree for the optimal curve
Δ	-15011568 = -1 · 24 · 38 · 11 · 13	Discriminant
Eigenvalues	2+ 3- -4 -4 11+ 13+ -4 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-9,189]	[a1,a2,a3,a4,a6]
Generators	[-3:15:1] [-2:15:1]	Generators of the group modulo torsion
j	-117649/20592	j-invariant
L	2.4076439729843	L(r)(E,1)/r!
Ω	1.8107150089299	Real period
R	0.66483238972175	Regulator
r	2	Rank of the group of rational points
S	1.0000000000002	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	20592bp1 82368co1 858m1 64350dz1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2574g1

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

---

Quadratic twists for elliptic curve 2574g1

-4	8	-3	5	-7	-11	13
20592bp1	82368co1	858m1	64350dz1	126126ci1	28314cj1	33462de1

---

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