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SageMath
E = EllipticCurve("cg1")
E.isogeny_class()
Elliptic curves in class 162240cg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 162240.cm2 | 162240cg1 | \([0, -1, 0, -568065, 173630625]\) | \(-16022066761/998400\) | \(-1263294508066406400\) | \([2]\) | \(2580480\) | \(2.2275\) | \(\Gamma_0(N)\)-optimal |
| 162240.cm1 | 162240cg2 | \([0, -1, 0, -9220865, 10780232865]\) | \(68523370149961/243360\) | \(307928036341186560\) | \([2]\) | \(5160960\) | \(2.5740\) |
Rank
sage: E.rank()
The elliptic curves in class 162240cg have rank \(1\).
Complex multiplication
The elliptic curves in class 162240cg do not have complex multiplication.Modular form 162240.2.a.cg
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.
