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SageMath
E = EllipticCurve("co1")
E.isogeny_class()
Elliptic curves in class 71148co
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 71148.bw2 | 71148co1 | \([0, 1, 0, -458509, 138751556]\) | \(-3196715008/649539\) | \(-2166055429450063536\) | \([2]\) | \(1296000\) | \(2.2407\) | \(\Gamma_0(N)\)-optimal |
| 71148.bw1 | 71148co2 | \([0, 1, 0, -7662244, 8160830852]\) | \(932410994128/29403\) | \(1568830269889757952\) | \([2]\) | \(2592000\) | \(2.5873\) |
Rank
sage: E.rank()
The elliptic curves in class 71148co have rank \(1\).
Complex multiplication
The elliptic curves in class 71148co do not have complex multiplication.Modular form 71148.2.a.co
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.
