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Properties

Label 337590bd
Number of curves $2$
Conductor $337590$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("bd1")
 
E.isogeny_class()
 

Elliptic curves in class 337590bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
337590.bd2 337590bd1 \([1, -1, 0, 2700, -789750]\) \(1685159/209250\) \(-270239672513250\) \([]\) \(1296000\) \(1.4486\) \(\Gamma_0(N)\)-optimal
337590.bd1 337590bd2 \([1, -1, 0, -569025, -165103515]\) \(-15777367606441/3574920\) \(-4616894671737480\) \([]\) \(3888000\) \(1.9979\)  

Rank

sage: E.rank()
 

The elliptic curves in class 337590bd have rank \(0\).

Complex multiplication

The elliptic curves in class 337590bd do not have complex multiplication.

Modular form 337590.2.a.bd

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} + q^{7} - q^{8} + q^{10} - 2 q^{13} - q^{14} + q^{16} - 5 q^{19} + O(q^{20})\) 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.