Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("bz1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 23104bz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
23104.bs3 23104bz1 \([0, -1, 0, 963, -829]\) \(32768/19\) \(-57207791296\) \([]\) \(17280\) \(0.75362\) \(\Gamma_0(N)\)-optimal
23104.bs2 23104bz2 \([0, -1, 0, -13477, -636189]\) \(-89915392/6859\) \(-20652012657856\) \([]\) \(51840\) \(1.3029\)  
23104.bs1 23104bz3 \([0, -1, 0, -1110917, -450312229]\) \(-50357871050752/19\) \(-57207791296\) \([]\) \(155520\) \(1.8522\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 23104.2.a.bz

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.