Properties

Label 23520.b
Number of curves $2$
Conductor $23520$
CM no
Rank $2$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 23520.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
23520.b1 23520e2 \([0, -1, 0, -961, 11761]\) \(69934528/225\) \(316108800\) \([2]\) \(16384\) \(0.49713\)  
23520.b2 23520e1 \([0, -1, 0, -86, 36]\) \(3241792/1875\) \(41160000\) \([2]\) \(8192\) \(0.15056\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 23520.b have rank \(2\).

Complex multiplication

The elliptic curves in class 23520.b do not have complex multiplication.

Modular form 23520.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + q^{9} - 6q^{11} - 4q^{13} + q^{15} + 2q^{17} - 4q^{19} + O(q^{20})\)  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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.