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SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 353780bn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 353780.bn1 | 353780bn1 | \([0, -1, 0, -16297465, 23623381062]\) | \(5405726654464/407253125\) | \(36065690708201492450000\) | \([2]\) | \(31104000\) | \(3.0735\) | \(\Gamma_0(N)\)-optimal |
| 353780.bn2 | 353780bn2 | \([0, -1, 0, 15631180, 104862625400]\) | \(298091207216/3525390625\) | \(-4995248020526522500000000\) | \([2]\) | \(62208000\) | \(3.4201\) |
Rank
sage: E.rank()
The elliptic curves in class 353780bn have rank \(1\).
Complex multiplication
The elliptic curves in class 353780bn do not have complex multiplication.Modular form 353780.2.a.bn
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.
