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SageMath
E = EllipticCurve("ct1")
E.isogeny_class()
Elliptic curves in class 25200ct
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 25200.j1 | 25200ct1 | \([0, 0, 0, -18447075, 30429857250]\) | \(551105805571803/1376829440\) | \(1734408567521280000000\) | \([2]\) | \(1935360\) | \(2.9528\) | \(\Gamma_0(N)\)-optimal |
| 25200.j2 | 25200ct2 | \([0, 0, 0, -11535075, 53509025250]\) | \(-134745327251163/903920796800\) | \(-1138679874778521600000000\) | \([2]\) | \(3870720\) | \(3.2994\) |
Rank
sage: E.rank()
The elliptic curves in class 25200ct have rank \(0\).
Complex multiplication
The elliptic curves in class 25200ct do not have complex multiplication.Modular form 25200.2.a.ct
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.
