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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 9702.bl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9702.bl1 | 9702bm2 | \([1, -1, 1, -2573465, 1589649401]\) | \(-448504189023625/135168\) | \(-568048917123072\) | \([3]\) | \(145152\) | \(2.1953\) | |
| 9702.bl2 | 9702bm1 | \([1, -1, 1, -26690, 2906705]\) | \(-500313625/574992\) | \(-2416426838855568\) | \([]\) | \(48384\) | \(1.6460\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9702.bl have rank \(1\).
Complex multiplication
The elliptic curves in class 9702.bl 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 LMFDB 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 LMFDB labels.
