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SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 389376.bn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 389376.bn1 | 389376bn3 | \([0, 0, 0, -984594, 376038520]\) | \(58591911104/243\) | \(437788023768576\) | \([2]\) | \(2764800\) | \(2.0188\) | |
| 389376.bn2 | 389376bn4 | \([0, 0, 0, -969384, 388218688]\) | \(-873722816/59049\) | \(-6808479345648893952\) | \([2]\) | \(5529600\) | \(2.3654\) | |
| 389376.bn3 | 389376bn1 | \([0, 0, 0, -11154, -439400]\) | \(85184/3\) | \(5404790416896\) | \([2]\) | \(552960\) | \(1.2141\) | \(\Gamma_0(N)\)-optimal |
| 389376.bn4 | 389376bn2 | \([0, 0, 0, 4056, -1546688]\) | \(64/9\) | \(-1037719760044032\) | \([2]\) | \(1105920\) | \(1.5606\) |
Rank
sage: E.rank()
The elliptic curves in class 389376.bn have rank \(0\).
Complex multiplication
The elliptic curves in class 389376.bn do not have complex multiplication.Modular form 389376.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
