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Properties

Label 388815bm
Number of curves $2$
Conductor $388815$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bm1")
 
E.isogeny_class()
 

Elliptic curves in class 388815bm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
388815.bm1 388815bm1 \([0, -1, 1, -552981, 489810656]\) \(-1073741824/5325075\) \(-92742966894490197075\) \([]\) \(10948608\) \(2.5158\) \(\Gamma_0(N)\)-optimal
388815.bm2 388815bm2 \([0, -1, 1, 4890429, -11985940723]\) \(742692847616/3992296875\) \(-69530937481838597296875\) \([]\) \(32845824\) \(3.0651\)  

Rank

sage: E.rank()
 

The elliptic curves in class 388815bm have rank \(1\).

Complex multiplication

The elliptic curves in class 388815bm do not have complex multiplication.

Modular form 388815.2.a.bm

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2 q^{4} - q^{5} + q^{9} - 3 q^{11} + 2 q^{12} + 4 q^{13} + q^{15} + 4 q^{16} - 6 q^{17} - q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.