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	2574b	Isogeny class
Conductor	2574	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	35328	Modular degree for the optimal curve
Δ	-308182905778176 = -1 · 212 · 33 · 118 · 13	Discriminant
Eigenvalues	2+ 3+ -2 -2 11- 13+ -8  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-937023,-348885875]	[a1,a2,a3,a4,a6]
j	-3369853043629824680811/11414181695488	j-invariant
L	0.61379291805879	L(r)(E,1)/r!
Ω	0.076724114757349	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	20592r1 82368f1 2574q1 64350dc1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2574b1

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

---

Quadratic twists for elliptic curve 2574b1

-4	8	-3	5	-7	-11	13
20592r1	82368f1	2574q1	64350dc1	126126bb1	28314bj1	33462bs1

---

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