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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 119952.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 119952.f1 | 119952fs2 | \([0, 0, 0, -2686719, 1694515354]\) | \(40685771728/14739\) | \(776990864553732864\) | \([]\) | \(3773952\) | \(2.4015\) | |
| 119952.f2 | 119952fs1 | \([0, 0, 0, -93639, -8100974]\) | \(1722448/459\) | \(24196947339043584\) | \([]\) | \(1257984\) | \(1.8521\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 119952.f have rank \(0\).
Complex multiplication
The elliptic curves in class 119952.f do not have complex multiplication.Modular form 119952.2.a.f
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.
