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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 458640z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
458640.z2 | 458640z1 | \([0, 0, 0, -18963, -1120238]\) | \(-57960603/8125\) | \(-105714685440000\) | \([2]\) | \(1474560\) | \(1.4223\) | \(\Gamma_0(N)\)-optimal* |
458640.z1 | 458640z2 | \([0, 0, 0, -312963, -67387838]\) | \(260549802603/4225\) | \(54971636428800\) | \([2]\) | \(2949120\) | \(1.7689\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 458640z have rank \(0\).
Complex multiplication
The elliptic curves in class 458640z do not have complex multiplication.Modular form 458640.2.a.z
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.