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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 72450n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
72450.c2 | 72450n1 | \([1, -1, 0, -26496492, -52486625584]\) | \(53514014005477719/3882876928\) | \(149270833152000000000\) | \([2]\) | \(6912000\) | \(2.9222\) | \(\Gamma_0(N)\)-optimal |
72450.c1 | 72450n2 | \([1, -1, 0, -423936492, -3359584865584]\) | \(219181950070420668759/1154048\) | \(44365482000000000\) | \([2]\) | \(13824000\) | \(3.2687\) |
Rank
sage: E.rank()
The elliptic curves in class 72450n have rank \(1\).
Complex multiplication
The elliptic curves in class 72450n do not have complex multiplication.Modular form 72450.2.a.n
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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.