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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 97461.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 97461.p1 | 97461n1 | \([1, -1, 0, -200664, 34629979]\) | \(10418796526321/6390657\) | \(548101861531497\) | \([2]\) | \(860160\) | \(1.7709\) | \(\Gamma_0(N)\)-optimal |
| 97461.p2 | 97461n2 | \([1, -1, 0, -163179, 47937154]\) | \(-5602762882081/8312741073\) | \(-712951556708587833\) | \([2]\) | \(1720320\) | \(2.1175\) |
Rank
sage: E.rank()
The elliptic curves in class 97461.p have rank \(0\).
Complex multiplication
The elliptic curves in class 97461.p do not have complex multiplication.Modular form 97461.2.a.p
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.
