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SageMath
E = EllipticCurve("fg1")
E.isogeny_class()
Elliptic curves in class 92736.fg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 92736.fg1 | 92736df1 | \([0, 0, 0, -714636, -232528112]\) | \(-5702623460245179/252448\) | \(-1786798669824\) | \([]\) | \(1013760\) | \(1.8330\) | \(\Gamma_0(N)\)-optimal |
| 92736.fg2 | 92736df2 | \([0, 0, 0, -654156, -273503088]\) | \(-5999796014211/2790817792\) | \(-14400006809173622784\) | \([]\) | \(3041280\) | \(2.3824\) |
Rank
sage: E.rank()
The elliptic curves in class 92736.fg have rank \(1\).
Complex multiplication
The elliptic curves in class 92736.fg do not have complex multiplication.Modular form 92736.2.a.fg
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.
