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Properties

Label 335730.dj
Number of curves $2$
Conductor $335730$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("dj1")
 
E.isogeny_class()
 

Elliptic curves in class 335730.dj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
335730.dj1 335730dj2 \([1, 0, 0, -13516750, -17844437500]\) \(5805223604235668521/435937500000000\) \(20509063748437500000000\) \([2]\) \(38707200\) \(3.0266\)  
335730.dj2 335730dj1 \([1, 0, 0, 807730, -1236635388]\) \(1238798620042199/14760960000000\) \(-694442367605760000000\) \([2]\) \(19353600\) \(2.6800\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 335730.dj have rank \(1\).

Complex multiplication

The elliptic curves in class 335730.dj do not have complex multiplication.

Modular form 335730.2.a.dj

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} + 2 q^{7} + q^{8} + q^{9} + q^{10} - 4 q^{11} + q^{12} + 4 q^{13} + 2 q^{14} + q^{15} + q^{16} - 6 q^{17} + q^{18} + O(q^{20})\) 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 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.