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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 29232n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 29232.j1 | 29232n1 | \([0, 0, 0, -66, -65]\) | \(2725888/1421\) | \(16574544\) | \([2]\) | \(5376\) | \(0.077134\) | \(\Gamma_0(N)\)-optimal |
| 29232.j2 | 29232n2 | \([0, 0, 0, 249, -506]\) | \(9148592/5887\) | \(-1098655488\) | \([2]\) | \(10752\) | \(0.42371\) |
Rank
sage: E.rank()
The elliptic curves in class 29232n have rank \(0\).
Complex multiplication
The elliptic curves in class 29232n do not have complex multiplication.Modular form 29232.2.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.
