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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 182070bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 182070.cp3 | 182070bb1 | \([1, -1, 1, -9158, 215237]\) | \(4826809/1680\) | \(29561763505680\) | \([2]\) | \(589824\) | \(1.2863\) | \(\Gamma_0(N)\)-optimal |
| 182070.cp2 | 182070bb2 | \([1, -1, 1, -61178, -5652619]\) | \(1439069689/44100\) | \(775996292024100\) | \([2, 2]\) | \(1179648\) | \(1.6329\) | |
| 182070.cp4 | 182070bb3 | \([1, -1, 1, 16852, -19136203]\) | \(30080231/9003750\) | \(-158432576288253750\) | \([2]\) | \(2359296\) | \(1.9795\) | |
| 182070.cp1 | 182070bb4 | \([1, -1, 1, -971528, -368336059]\) | \(5763259856089/5670\) | \(99770951831670\) | \([2]\) | \(2359296\) | \(1.9795\) |
Rank
sage: E.rank()
The elliptic curves in class 182070bb have rank \(0\).
Complex multiplication
The elliptic curves in class 182070bb do not have complex multiplication.Modular form 182070.2.a.bb
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
