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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 97461.u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 97461.u1 | 97461j1 | \([1, -1, 0, -5742, 11479]\) | \(244140625/140777\) | \(12073897216017\) | \([2]\) | \(147456\) | \(1.1997\) | \(\Gamma_0(N)\)-optimal |
| 97461.u2 | 97461j2 | \([1, -1, 0, 22923, 74542]\) | \(15531437375/9020557\) | \(-773658183149397\) | \([2]\) | \(294912\) | \(1.5463\) |
Rank
sage: E.rank()
The elliptic curves in class 97461.u have rank \(0\).
Complex multiplication
The elliptic curves in class 97461.u do not have complex multiplication.Modular form 97461.2.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.
