Properties

Label 43350.ba
Number of curves $2$
Conductor $43350$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ba1")
 
E.isogeny_class()
 

Elliptic curves in class 43350.ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
43350.ba1 43350bj2 \([1, 0, 1, -3253101, -2258637152]\) \(-843137281012581793/216\) \(-975375000\) \([]\) \(734832\) \(2.0073\)  
43350.ba2 43350bj1 \([1, 0, 1, -40101, -3111152]\) \(-1579268174113/10077696\) \(-45507096000000\) \([]\) \(244944\) \(1.4580\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 43350.ba have rank \(0\).

Complex multiplication

The elliptic curves in class 43350.ba do not have complex multiplication.

Modular form 43350.2.a.ba

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} - 4 q^{7} - q^{8} + q^{9} - 3 q^{11} + q^{12} - 2 q^{13} + 4 q^{14} + q^{16} - q^{18} + 8 q^{19} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.