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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 81120bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 81120.d2 | 81120bd1 | \([0, -1, 0, -11886, 831336]\) | \(-601211584/609375\) | \(-188245551000000\) | \([2]\) | \(322560\) | \(1.4346\) | \(\Gamma_0(N)\)-optimal |
| 81120.d1 | 81120bd2 | \([0, -1, 0, -223136, 40630836]\) | \(497169541448/190125\) | \(469860895296000\) | \([2]\) | \(645120\) | \(1.7812\) |
Rank
sage: E.rank()
The elliptic curves in class 81120bd have rank \(2\).
Complex multiplication
The elliptic curves in class 81120bd do not have complex multiplication.Modular form 81120.2.a.bd
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.
