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SageMath
E = EllipticCurve("ge1")
E.isogeny_class()
Elliptic curves in class 106722.ge
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
106722.ge1 | 106722gm2 | \([1, -1, 1, -153572, 24071303]\) | \(-6329617441/279936\) | \(-17714890491129216\) | \([]\) | \(799680\) | \(1.8827\) | |
106722.ge2 | 106722gm1 | \([1, -1, 1, -1112, -32623]\) | \(-2401/6\) | \(-379691582886\) | \([]\) | \(114240\) | \(0.90978\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 106722.ge have rank \(1\).
Complex multiplication
The elliptic curves in class 106722.ge do not have complex multiplication.Modular form 106722.2.a.ge
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.