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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 33462bh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 33462.g2 | 33462bh1 | \([1, -1, 0, -9918, 548640]\) | \(-30664297/18876\) | \(-66419807232636\) | \([2]\) | \(107520\) | \(1.3541\) | \(\Gamma_0(N)\)-optimal |
| 33462.g1 | 33462bh2 | \([1, -1, 0, -177228, 28757106]\) | \(174958262857/33462\) | \(117744203730582\) | \([2]\) | \(215040\) | \(1.7007\) |
Rank
sage: E.rank()
The elliptic curves in class 33462bh have rank \(1\).
Complex multiplication
The elliptic curves in class 33462bh do not have complex multiplication.Modular form 33462.2.a.bh
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.
