Properties

Label 338100.bj
Number of curves $2$
Conductor $338100$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bj1")
 
E.isogeny_class()
 

Elliptic curves in class 338100.bj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
338100.bj1 338100bj1 \([0, -1, 0, -310333, -67321463]\) \(-280944640/4347\) \(-51142020300000000\) \([]\) \(3732480\) \(2.0082\) \(\Gamma_0(N)\)-optimal
338100.bj2 338100bj2 \([0, -1, 0, 1159667, -331921463]\) \(14660034560/12519843\) \(-147294700910700000000\) \([]\) \(11197440\) \(2.5575\)  

Rank

sage: E.rank()
 

The elliptic curves in class 338100.bj have rank \(0\).

Complex multiplication

The elliptic curves in class 338100.bj do not have complex multiplication.

Modular form 338100.2.a.bj

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{9} + 4 q^{13} - 6 q^{17} + 7 q^{19} + O(q^{20})\) 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 LMFDB 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 LMFDB labels.