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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 138600g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 138600.cz1 | 138600g1 | \([0, 0, 0, -999750, -384746875]\) | \(4850878539776/130977\) | \(2983819781250000\) | \([2]\) | \(1331200\) | \(2.0737\) | \(\Gamma_0(N)\)-optimal |
| 138600.cz2 | 138600g2 | \([0, 0, 0, -960375, -416443750]\) | \(-268750151696/50014503\) | \(-18230286343500000000\) | \([2]\) | \(2662400\) | \(2.4202\) |
Rank
sage: E.rank()
The elliptic curves in class 138600g have rank \(1\).
Complex multiplication
The elliptic curves in class 138600g do not have complex multiplication.Modular form 138600.2.a.g
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
