Elliptic curve isogeny class with Cremona label 225318ba (LMFDB label 225318.l)

• Label: 225318ba
• Number of curves: $4$
• Conductor: $225318$
• CM: no
• Rank: $1$

Elliptic curves in class 225318ba

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
225318.l2	225318ba1	\([1, 0, 1, -564446, -163209328]\)	\(1845026709625/793152\)	\(8549556196627008\)	\([2]\)	\(2384640\)	\(2.0172\)	\(\Gamma_0(N)\)-optimal
225318.l3	225318ba2	\([1, 0, 1, -476086, -216013264]\)	\(-1107111813625/1228691592\)	\(-13244331243099813768\)	\([2]\)	\(4769280\)	\(2.3638\)
225318.l1	225318ba3	\([1, 0, 1, -1657901, 621056360]\)	\(46753267515625/11591221248\)	\(124944269758272110592\)	\([2]\)	\(7153920\)	\(2.5665\)
225318.l4	225318ba4	\([1, 0, 1, 3997139, 3939433832]\)	\(655215969476375/1001033261568\)	\(-10790353077932652175872\)	\([2]\)	\(14307840\)	\(2.9131\)

Rank

The elliptic curves in class 225318ba have rank \(1\).

Complex multiplication

The elliptic curves in class 225318ba do not have complex multiplication.

Modular form 225318.2.a.ba

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.