Properties

Label 142800.bm
Number of curves $4$
Conductor $142800$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bm1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 142800.bm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
142800.bm1 142800ev4 \([0, -1, 0, -2031608, -1113894288]\) \(14489843500598257/6246072\) \(399748608000000\) \([2]\) \(2359296\) \(2.1444\)  
142800.bm2 142800ev3 \([0, -1, 0, -271608, 28889712]\) \(34623662831857/14438442312\) \(924060307968000000\) \([2]\) \(2359296\) \(2.1444\)  
142800.bm3 142800ev2 \([0, -1, 0, -127608, -17190288]\) \(3590714269297/73410624\) \(4698279936000000\) \([2, 2]\) \(1179648\) \(1.7978\)  
142800.bm4 142800ev1 \([0, -1, 0, 392, -806288]\) \(103823/4386816\) \(-280756224000000\) \([2]\) \(589824\) \(1.4513\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 142800.bm have rank \(0\).

Complex multiplication

The elliptic curves in class 142800.bm do not have complex multiplication.

Modular form 142800.2.a.bm

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{7} + q^{9} + 6q^{13} - q^{17} + O(q^{20})\)  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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.