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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 58800bh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 58800.k2 | 58800bh1 | \([0, -1, 0, 5717, -1013438]\) | \(2048/45\) | \(-453978078750000\) | \([2]\) | \(258048\) | \(1.4927\) | \(\Gamma_0(N)\)-optimal |
| 58800.k1 | 58800bh2 | \([0, -1, 0, -122908, -15676688]\) | \(1272112/75\) | \(12106082100000000\) | \([2]\) | \(516096\) | \(1.8393\) |
Rank
sage: E.rank()
The elliptic curves in class 58800bh have rank \(0\).
Complex multiplication
The elliptic curves in class 58800bh do not have complex multiplication.Modular form 58800.2.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.
