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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 176400bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 176400.jj2 | 176400bg1 | \([0, 0, 0, -28875, -1583750]\) | \(46585/8\) | \(457228800000000\) | \([]\) | \(622080\) | \(1.5334\) | \(\Gamma_0(N)\)-optimal |
| 176400.jj1 | 176400bg2 | \([0, 0, 0, -658875, 205686250]\) | \(553463785/512\) | \(29262643200000000\) | \([]\) | \(1866240\) | \(2.0827\) |
Rank
sage: E.rank()
The elliptic curves in class 176400bg have rank \(1\).
Complex multiplication
The elliptic curves in class 176400bg do not have complex multiplication.Modular form 176400.2.a.bg
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 Cremona 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 Cremona labels.
