Cremona's table of elliptic curves

558 = 2 · 3² · 31

Field	Data	Notes
Atkin-Lehner	2- 3+ 31-	Signs for the Atkin-Lehner involutions
Class	558f	Isogeny class
Conductor	558	Conductor
∏ cp	30	Product of Tamagawa factors cp
deg	240	Modular degree for the optimal curve
Δ	-27426816 = -1 · 215 · 33 · 31	Discriminant
Eigenvalues	2- 3+ -3 -4 -3  5 -3 -7	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,46,209]	[a1,a2,a3,a4,a6]
Generators	[-3:7:1]	Generators of the group modulo torsion
j	406869021/1015808	j-invariant
L	2.3825303331677	L(r)(E,1)/r!
Ω	1.4723271192317	Real period
R	0.4854621575695	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	4464n1 17856i1 558b2 13950i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 558f1

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
-	+	-3	-4	-3	5	-3	-7	-6	-6	-	2	12	8	3	-12	-6	5	11	3	-4	-13	3	6	-7

---

Quadratic twists for elliptic curve 558f1

-4	8	-3	5	-7	-11	13	-31
4464n1	17856i1	558b2	13950i1	27342w1	67518f1	94302d1	17298n1

---

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