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SageMath
E = EllipticCurve("mt1")
E.isogeny_class()
Elliptic curves in class 446400.mt
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
446400.mt1 | 446400mt2 | \([0, 0, 0, -7524300, 7945702000]\) | \(-15777367606441/3574920\) | \(-10674653921280000000\) | \([]\) | \(13271040\) | \(2.6434\) | \(\Gamma_0(N)\)-optimal* |
446400.mt2 | 446400mt1 | \([0, 0, 0, 35700, 37942000]\) | \(1685159/209250\) | \(-624817152000000000\) | \([]\) | \(4423680\) | \(2.0940\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 446400.mt have rank \(1\).
Complex multiplication
The elliptic curves in class 446400.mt do not have complex multiplication.Modular form 446400.2.a.mt
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.