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SageMath
E = EllipticCurve("co1")
E.isogeny_class()
Elliptic curves in class 23232co
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 23232.w2 | 23232co1 | \([0, -1, 0, -275073, -24626655]\) | \(3723875/1728\) | \(1068114538672422912\) | \([2]\) | \(304128\) | \(2.1539\) | \(\Gamma_0(N)\)-optimal |
| 23232.w1 | 23232co2 | \([0, -1, 0, -3682433, -2717122527]\) | \(8934171875/5832\) | \(3604886568019427328\) | \([2]\) | \(608256\) | \(2.5005\) |
Rank
sage: E.rank()
The elliptic curves in class 23232co have rank \(0\).
Complex multiplication
The elliptic curves in class 23232co do not have complex multiplication.Modular form 23232.2.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.
