Cremona's table of elliptic curves

858 = 2 · 3 · 11 · 13

Field	Data	Notes
Atkin-Lehner	2+ 3+ 11- 13+	Signs for the Atkin-Lehner involutions
Class	858a	Isogeny class
Conductor	858	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	106007616 = 26 · 34 · 112 · 132	Discriminant
Eigenvalues	2+ 3+  2  0 11- 13+  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-314,-2220]	[a1,a2,a3,a4,a6]
j	3440899317673/106007616	j-invariant
L	1.1358111271594	L(r)(E,1)/r!
Ω	1.1358111271594	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	6864u2 27456bc2 2574t2 21450cp2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 858a2

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 858a2

-4	8	-3	5	-7	-11	13
6864u2	27456bc2	2574t2	21450cp2	42042bt2	9438v2	11154w2

---

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