Properties

Label 23104.bi
Number of curves $2$
Conductor $23104$
CM no
Rank $2$
Graph

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Show commands: SageMath
E = EllipticCurve("bi1")
 
E.isogeny_class()
 

Elliptic curves in class 23104.bi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
23104.bi1 23104n2 \([0, 1, 0, -5953, 175135]\) \(-246579625/512\) \(-48452599808\) \([]\) \(20736\) \(0.93613\)  
23104.bi2 23104n1 \([0, 1, 0, 127, 1247]\) \(2375/8\) \(-757071872\) \([]\) \(6912\) \(0.38682\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 23104.bi have rank \(2\).

Complex multiplication

The elliptic curves in class 23104.bi do not have complex multiplication.

Modular form 23104.2.a.bi

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