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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)
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.