Properties

Label 18240bp
Number of curves $2$
Conductor $18240$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bp1")
 
E.isogeny_class()
 

Elliptic curves in class 18240bp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
18240.cy2 18240bp1 \([0, 1, 0, -6305, 209343]\) \(-105756712489/12476160\) \(-3270550487040\) \([2]\) \(36864\) \(1.1371\) \(\Gamma_0(N)\)-optimal
18240.cy1 18240bp2 \([0, 1, 0, -103585, 12797375]\) \(468898230633769/5540400\) \(1452382617600\) \([2]\) \(73728\) \(1.4837\)  

Rank

sage: E.rank()
 

The elliptic curves in class 18240bp have rank \(0\).

Complex multiplication

The elliptic curves in class 18240bp do not have complex multiplication.

Modular form 18240.2.a.bp

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} + 2 q^{7} + q^{9} + 6 q^{11} + q^{15} + 2 q^{17} + q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.