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SageMath
E = EllipticCurve("gb1")
E.isogeny_class()
Elliptic curves in class 176400.gb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 176400.gb1 | 176400y1 | \([0, 0, 0, -1203195, -505256150]\) | \(4386781853/27216\) | \(1195115903557632000\) | \([2]\) | \(2949120\) | \(2.3068\) | \(\Gamma_0(N)\)-optimal |
| 176400.gb2 | 176400y2 | \([0, 0, 0, -497595, -1093020950]\) | \(-310288733/11573604\) | \(-508223037987883008000\) | \([2]\) | \(5898240\) | \(2.6533\) |
Rank
sage: E.rank()
The elliptic curves in class 176400.gb have rank \(1\).
Complex multiplication
The elliptic curves in class 176400.gb do not have complex multiplication.Modular form 176400.2.a.gb
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.
