Properties

Label 333270.p
Number of curves $2$
Conductor $333270$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 333270.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
333270.p1 333270p2 \([1, -1, 0, -21371400, -38260237464]\) \(-2799235530137373837169/20348876953125000\) \(-7847361257080078125000\) \([]\) \(24883200\) \(3.0331\)  
333270.p2 333270p1 \([1, -1, 0, 761040, -279763200]\) \(126404531110923791/160707758400000\) \(-61975500657134400000\) \([]\) \(8294400\) \(2.4838\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 333270.p have rank \(1\).

Complex multiplication

The elliptic curves in class 333270.p do not have complex multiplication.

Modular form 333270.2.a.p

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