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Properties

Label 193614.bd
Number of curves $2$
Conductor $193614$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bd1")
 
E.isogeny_class()
 

Elliptic curves in class 193614.bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
193614.bd1 193614e2 \([1, 0, 0, -272446, 68770514]\) \(-15107691357361/5067577806\) \(-750183385587879534\) \([]\) \(3267000\) \(2.1419\)  
193614.bd2 193614e1 \([1, 0, 0, -2656, -406816]\) \(-13997521/474336\) \(-70218751444704\) \([]\) \(653400\) \(1.3372\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 193614.bd have rank \(0\).

Complex multiplication

The elliptic curves in class 193614.bd do not have complex multiplication.

Modular form 193614.2.a.bd

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + 2 q^{7} + q^{8} + q^{9} - q^{10} - 2 q^{11} + q^{12} + 4 q^{13} + 2 q^{14} - q^{15} + q^{16} + 7 q^{17} + q^{18} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.