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SageMath
E = EllipticCurve("ln1")
E.isogeny_class()
Elliptic curves in class 273600ln
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 273600.ln2 | 273600ln1 | \([0, 0, 0, 180, -32400]\) | \(27/19\) | \(-453869568000\) | \([2]\) | \(262144\) | \(0.91580\) | \(\Gamma_0(N)\)-optimal |
| 273600.ln1 | 273600ln2 | \([0, 0, 0, -14220, -637200]\) | \(13312053/361\) | \(8623521792000\) | \([2]\) | \(524288\) | \(1.2624\) |
Rank
sage: E.rank()
The elliptic curves in class 273600ln have rank \(1\).
Complex multiplication
The elliptic curves in class 273600ln do not have complex multiplication.Modular form 273600.2.a.ln
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.
