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SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 33462bn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 33462.w2 | 33462bn1 | \([1, -1, 0, -875367, -1100073155]\) | \(-9595703125/62099136\) | \(-480068551357588619712\) | \([2]\) | \(898560\) | \(2.6518\) | \(\Gamma_0(N)\)-optimal |
| 33462.w1 | 33462bn2 | \([1, -1, 0, -22230207, -40252036811]\) | \(157158018407125/382657176\) | \(2958200193782178022392\) | \([2]\) | \(1797120\) | \(2.9984\) |
Rank
sage: E.rank()
The elliptic curves in class 33462bn have rank \(0\).
Complex multiplication
The elliptic curves in class 33462bn do not have complex multiplication.Modular form 33462.2.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.
