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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 317900bh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 317900.bh1 | 317900bh1 | \([0, -1, 0, -1107833, 449249162]\) | \(-996720640/187\) | \(-28210783768750000\) | \([]\) | \(3110400\) | \(2.1583\) | \(\Gamma_0(N)\)-optimal |
| 317900.bh2 | 317900bh2 | \([0, -1, 0, 337167, 1509156662]\) | \(28098560/6539203\) | \(-986502897609418750000\) | \([]\) | \(9331200\) | \(2.7076\) |
Rank
sage: E.rank()
The elliptic curves in class 317900bh have rank \(0\).
Complex multiplication
The elliptic curves in class 317900bh do not have complex multiplication.Modular form 317900.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
