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	858d	Isogeny class
Conductor	858	Conductor
∏ cp	18	Product of Tamagawa factors cp
deg	3120	Modular degree for the optimal curve
Δ	-103332962304 = -1 · 213 · 36 · 113 · 13	Discriminant
Eigenvalues	2+ 3-  3 -1 11- 13-  0  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-103987,12897998]	[a1,a2,a3,a4,a6]
j	-124352595912593543977/103332962304	j-invariant
L	1.7694033452319	L(r)(E,1)/r!
Ω	0.88470167261597	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	6864o1 27456e1 2574v1 21450bt1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 858d1

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	-1	-	-	0	2	3	-3	8	2	-9	5	0	-6	-3	-1	11	-6	-1	2	18	0	2

---

Quadratic twists for elliptic curve 858d1

-4	8	-3	5	-7	-11	13
6864o1	27456e1	2574v1	21450bt1	42042v1	9438bd1	11154be1

---

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