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	2574t	Isogeny class
Conductor	2574	Conductor
∏ cp	48	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	-3842961408 = -1 · 212 · 38 · 11 · 13	Discriminant
Eigenvalues	2- 3- -2  0 11+ 13+ -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,49,2967]	[a1,a2,a3,a4,a6]
Generators	[-1:54:1]	Generators of the group modulo torsion
j	18191447/5271552	j-invariant
L	4.1984950971444	L(r)(E,1)/r!
Ω	1.0817019433008	Real period
R	0.32344824153782	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	20592bn1 82368ch1 858a1 64350bc1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2574t1

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

---

Quadratic twists for elliptic curve 2574t1

-4	8	-3	5	-7	-11	13
20592bn1	82368ch1	858a1	64350bc1	126126ff1	28314ba1	33462bg1

---

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