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SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 50715bn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 50715.br1 | 50715bn1 | \([1, -1, 0, -101439, -10660280]\) | \(1345938541921/203765625\) | \(17476187249390625\) | \([2]\) | \(294912\) | \(1.8406\) | \(\Gamma_0(N)\)-optimal |
| 50715.br2 | 50715bn2 | \([1, -1, 0, 174186, -58674155]\) | \(6814692748079/21258460125\) | \(-1823255663354425125\) | \([2]\) | \(589824\) | \(2.1872\) |
Rank
sage: E.rank()
The elliptic curves in class 50715bn have rank \(0\).
Complex multiplication
The elliptic curves in class 50715bn do not have complex multiplication.Modular form 50715.2.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.
