Properties

Label 277200bf
Number of curves $4$
Conductor $277200$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("bf1")
 
E.isogeny_class()
 

Elliptic curves in class 277200bf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
277200.bf3 277200bf1 \([0, 0, 0, -16050, 667375]\) \(2508888064/396165\) \(72201071250000\) \([2]\) \(589824\) \(1.3820\) \(\Gamma_0(N)\)-optimal
277200.bf2 277200bf2 \([0, 0, 0, -71175, -6664250]\) \(13674725584/1334025\) \(3890016900000000\) \([2, 2]\) \(1179648\) \(1.7285\)  
277200.bf4 277200bf3 \([0, 0, 0, 86325, -32021750]\) \(6099383804/41507235\) \(-484140389040000000\) \([2]\) \(2359296\) \(2.0751\)  
277200.bf1 277200bf4 \([0, 0, 0, -1110675, -450530750]\) \(12990838708516/144375\) \(1683990000000000\) \([2]\) \(2359296\) \(2.0751\)  

Rank

sage: E.rank()
 

The elliptic curves in class 277200bf have rank \(0\).

Complex multiplication

The elliptic curves in class 277200bf do not have complex multiplication.

Modular form 277200.2.a.bf

sage: E.q_eigenform(10)
 
\(q - q^{7} - q^{11} - 2 q^{13} + 6 q^{17} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().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

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.