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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 142956o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 142956.v1 | 142956o1 | \([0, 0, 0, -433200, 110265284]\) | \(-1024000000/5643\) | \(-49544922067483392\) | \([]\) | \(1036800\) | \(2.0468\) | \(\Gamma_0(N)\)-optimal |
| 142956.v2 | 142956o2 | \([0, 0, 0, 1126320, 587322452]\) | \(17997824000/27387987\) | \(-240463526758860227328\) | \([]\) | \(3110400\) | \(2.5961\) |
Rank
sage: E.rank()
The elliptic curves in class 142956o have rank \(1\).
Complex multiplication
The elliptic curves in class 142956o do not have complex multiplication.Modular form 142956.2.a.o
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.
