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Properties

Label 79350.bw
Number of curves $2$
Conductor $79350$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bw1")
 
E.isogeny_class()
 

Elliptic curves in class 79350.bw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
79350.bw1 79350bv2 \([1, 0, 1, -123326, 16928048]\) \(-1003845508585/18874368\) \(-3900211200000000\) \([]\) \(725760\) \(1.7865\)  
79350.bw2 79350bv1 \([1, 0, 1, 6049, 109298]\) \(118484615/93312\) \(-19282050000000\) \([]\) \(241920\) \(1.2371\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 79350.bw have rank \(0\).

Complex multiplication

The elliptic curves in class 79350.bw do not have complex multiplication.

Modular form 79350.2.a.bw

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} + 4 q^{7} - q^{8} + q^{9} + 3 q^{11} + q^{12} - 4 q^{13} - 4 q^{14} + q^{16} - 3 q^{17} - q^{18} + 4 q^{19} + O(q^{20})\) 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.