Properties

Label 23520.bc
Number of curves $2$
Conductor $23520$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bc1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 23520.bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
23520.bc1 23520p1 \([0, 1, 0, -10306, 329300]\) \(16079333824/2953125\) \(22235661000000\) \([2]\) \(55296\) \(1.2795\) \(\Gamma_0(N)\)-optimal
23520.bc2 23520p2 \([0, 1, 0, 20319, 1940175]\) \(1925134784/4465125\) \(-2151700443648000\) \([2]\) \(110592\) \(1.6261\)  

Rank

sage: E.rank()
 

The elliptic curves in class 23520.bc have rank \(1\).

Complex multiplication

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

Modular form 23520.2.a.bc

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