Properties

Label 18480.bc
Number of curves $2$
Conductor $18480$
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 18480.bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
18480.bc1 18480cb2 \([0, -1, 0, -428645, 2042286477]\) \(-2126464142970105856/438611057788643355\) \(-1796550892702283182080\) \([]\) \(1200000\) \(2.7576\)  
18480.bc2 18480cb1 \([0, -1, 0, -143045, -24338643]\) \(-79028701534867456/16987307596875\) \(-69580011916800000\) \([]\) \(240000\) \(1.9529\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 18480.bc have rank \(1\).

Complex multiplication

The elliptic curves in class 18480.bc do not have complex multiplication.

Modular form 18480.2.a.bc

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} - q^{7} + q^{9} - q^{11} - 6q^{13} - q^{15} - 7q^{17} + 5q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.