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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 9702bl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9702.bh2 | 9702bl1 | \([1, -1, 1, -128981, -17817299]\) | \(-35148950502093/46137344\) | \(-311485620289536\) | \([2]\) | \(59136\) | \(1.6878\) | \(\Gamma_0(N)\)-optimal |
| 9702.bh1 | 9702bl2 | \([1, -1, 1, -2064341, -1141100243]\) | \(144106117295241933/247808\) | \(1673018468352\) | \([2]\) | \(118272\) | \(2.0344\) |
Rank
sage: E.rank()
The elliptic curves in class 9702bl have rank \(0\).
Complex multiplication
The elliptic curves in class 9702bl do not have complex multiplication.Modular form 9702.2.a.bl
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.
