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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 9702.u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9702.u1 | 9702e2 | \([1, -1, 0, -229371, 42339429]\) | \(144106117295241933/247808\) | \(2294949888\) | \([2]\) | \(39424\) | \(1.4851\) | |
| 9702.u2 | 9702e1 | \([1, -1, 0, -14331, 664677]\) | \(-35148950502093/46137344\) | \(-427277942784\) | \([2]\) | \(19712\) | \(1.1385\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9702.u have rank \(0\).
Complex multiplication
The elliptic curves in class 9702.u do not have complex multiplication.Modular form 9702.2.a.u
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
