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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 97461.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 97461.k1 | 97461i1 | \([1, -1, 1, -20075, 1033386]\) | \(10431681625/710073\) | \(60900206836833\) | \([2]\) | \(294912\) | \(1.3935\) | \(\Gamma_0(N)\)-optimal |
| 97461.k2 | 97461i2 | \([1, -1, 1, 17410, 4422030]\) | \(6804992375/102626433\) | \(-8801871070476393\) | \([2]\) | \(589824\) | \(1.7401\) |
Rank
sage: E.rank()
The elliptic curves in class 97461.k have rank \(1\).
Complex multiplication
The elliptic curves in class 97461.k do not have complex multiplication.Modular form 97461.2.a.k
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.
