Properties

Label 23104.q
Number of curves $3$
Conductor $23104$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 23104.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
23104.q1 23104bt3 \([0, -1, 0, -1975873, -8598438175]\) \(-69173457625/2550136832\) \(-31450315864667322318848\) \([]\) \(1244160\) \(2.9971\)  
23104.q2 23104bt1 \([0, -1, 0, -358593, 82797409]\) \(-413493625/152\) \(-1874584905187328\) \([]\) \(138240\) \(1.8985\) \(\Gamma_0(N)\)-optimal
23104.q3 23104bt2 \([0, -1, 0, 219007, 314091553]\) \(94196375/3511808\) \(-43310409649448026112\) \([]\) \(414720\) \(2.4478\)  

Rank

sage: E.rank()
 

The elliptic curves in class 23104.q have rank \(1\).

Complex multiplication

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

Modular form 23104.2.a.q

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{7} - 2 q^{9} - 6 q^{11} + 5 q^{13} + 3 q^{17} + O(q^{20})\) 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.

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.