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	2574m	Isogeny class
Conductor	2574	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	-7668846009015048 = -1 · 23 · 318 · 114 · 132	Discriminant
Eigenvalues	2+ 3- -2  4 11- 13+ -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,48357,-1012019]	[a1,a2,a3,a4,a6]
Generators	[29:629:1]	Generators of the group modulo torsion
j	17154149157653327/10519679024712	j-invariant
L	2.4051396830572	L(r)(E,1)/r!
Ω	0.24116019156586	Real period
R	1.2466504460379	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	20592bc4 82368bh3 858e4 64350es3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2574m4

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	4	-	+	-2	-4	-4	2	0	-2	-10	-4	4	-2	4	10	-4	-12	2	-4	12	-2	2

---

Quadratic twists for elliptic curve 2574m4

-4	8	-3	5	-7	-11	13
20592bc4	82368bh3	858e4	64350es3	126126dc3	28314ch3	33462cj3

---

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