Properties

Label 705600.lx
Number of curves $2$
Conductor $705600$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("lx1")
 
E.isogeny_class()
 

Elliptic curves in class 705600.lx

sage: E.isogeny_class().curves
 
LMFDB label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height
705600.lx1 \([0, 0, 0, -7070700, -7237006000]\) \(-5452947409/250\) \(-1792336896000000000\) \([]\) \(19906560\) \(2.5781\)
705600.lx2 \([0, 0, 0, -14700, -25774000]\) \(-49/40\) \(-286773903360000000\) \([]\) \(6635520\) \(2.0288\)

Rank

sage: E.rank()
 

The elliptic curves in class 705600.lx have rank \(1\).

Complex multiplication

The elliptic curves in class 705600.lx do not have complex multiplication.

Modular form 705600.2.a.lx

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