Elliptic curve isogeny class with Cremona label 49098bo (LMFDB label 49098.bp)

• Label: 49098bo
• Number of curves: $4$
• Conductor: $49098$
• CM: no
• Rank: $1$

Elliptic curves in class 49098bo

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
49098.bp4	49098bo1	\([1, 0, 0, 73058, 16385732]\)	\(366554400441263/1197281046528\)	\(-140858917842972672\)	\([2]\)	\(774144\)	\(1.9737\)	\(\Gamma_0(N)\)-optimal
49098.bp3	49098bo2	\([1, 0, 0, -695262, 192638340]\)	\(315922815546536017/46479778841664\)	\(5468299500942927936\)	\([2, 2]\)	\(1548288\)	\(2.3203\)
49098.bp2	49098bo3	\([1, 0, 0, -2986502, -1796616228]\)	\(25039399590518087377/2641281025170312\)	\(310744071330262036488\)	\([2]\)	\(3096576\)	\(2.6668\)
49098.bp1	49098bo4	\([1, 0, 0, -10697142, 13465133100]\)	\(1150638118585800835537/31752757008504\)	\(3735680109293487096\)	\([2]\)	\(3096576\)	\(2.6668\)

Rank

The elliptic curves in class 49098bo have rank \(1\).

Complex multiplication

The elliptic curves in class 49098bo do not have complex multiplication.

Modular form 49098.2.a.bo

Isogeny matrix

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.