Elliptic curve isogeny class with Cremona label 180336cr (LMFDB label 180336.g)

• Label: 180336cr
• Number of curves: $4$
• Conductor: $180336$
• CM: no
• Rank: $2$

Elliptic curves in class 180336cr

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
180336.g3	180336cr1	\([0, -1, 0, -129279, -15496362]\)	\(618724784128/87947613\)	\(33965465234764752\)	\([2]\)	\(1474560\)	\(1.8978\)	\(\Gamma_0(N)\)-optimal
180336.g2	180336cr2	\([0, -1, 0, -546884, 140353824]\)	\(2927363579728/320445801\)	\(1980104353893828864\)	\([2, 2]\)	\(2949120\)	\(2.2444\)
180336.g1	180336cr3	\([0, -1, 0, -8505944, 9551146368]\)	\(2753580869496292/39328497\)	\(972077373443884032\)	\([4]\)	\(5898240\)	\(2.5910\)
180336.g4	180336cr4	\([0, -1, 0, 730496, 697291504]\)	\(1744147297148/9513325341\)	\(-235139631961944093696\)	\([2]\)	\(5898240\)	\(2.5910\)

Rank

The elliptic curves in class 180336cr have rank \(2\).

Complex multiplication

The elliptic curves in class 180336cr do not have complex multiplication.

Modular form 180336.2.a.cr

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.