Elliptic curve isogeny class with Cremona label 61200eu (LMFDB label 61200.ft)

• Label: 61200eu
• Number of curves: $4$
• Conductor: $61200$
• CM: no
• Rank: $1$

Elliptic curves in class 61200eu

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
61200.ft2	61200eu1	\([0, 0, 0, -919875, 339453250]\)	\(1845026709625/793152\)	\(37005299712000000\)	\([2]\)	\(663552\)	\(2.1393\)	\(\Gamma_0(N)\)-optimal
61200.ft3	61200eu2	\([0, 0, 0, -775875, 449325250]\)	\(-1107111813625/1228691592\)	\(-57325834916352000000\)	\([2]\)	\(1327104\)	\(2.4859\)
61200.ft1	61200eu3	\([0, 0, 0, -2701875, -1292372750]\)	\(46753267515625/11591221248\)	\(540800018546688000000\)	\([2]\)	\(1990656\)	\(2.6886\)
61200.ft4	61200eu4	\([0, 0, 0, 6514125, -8195156750]\)	\(655215969476375/1001033261568\)	\(-46704207851716608000000\)	\([2]\)	\(3981312\)	\(3.0352\)

Rank

The elliptic curves in class 61200eu have rank \(1\).

Complex multiplication

The elliptic curves in class 61200eu do not have complex multiplication.

Modular form 61200.2.a.eu

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.