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SageMath
E = EllipticCurve("ci1")
E.isogeny_class()
Elliptic curves in class 182070.ci
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 182070.ci1 | 182070bn2 | \([1, -1, 1, -1348673, -443775463]\) | \(15417797707369/4080067320\) | \(71794038810174763320\) | \([2]\) | \(5308416\) | \(2.5186\) | |
| 182070.ci2 | 182070bn1 | \([1, -1, 1, 211927, -44886103]\) | \(59822347031/83966400\) | \(-1477496940013886400\) | \([2]\) | \(2654208\) | \(2.1720\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 182070.ci have rank \(1\).
Complex multiplication
The elliptic curves in class 182070.ci do not have complex multiplication.Modular form 182070.2.a.ci
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
