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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 230640o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 230640.o2 | 230640o1 | \([0, -1, 0, -630736, -197564480]\) | \(-7633736209/230640\) | \(-838426005446000640\) | \([2]\) | \(3686400\) | \(2.2170\) | \(\Gamma_0(N)\)-optimal |
| 230640.o1 | 230640o2 | \([0, -1, 0, -10163856, -12468596544]\) | \(31942518433489/27900\) | \(101422500658790400\) | \([2]\) | \(7372800\) | \(2.5636\) |
Rank
sage: E.rank()
The elliptic curves in class 230640o have rank \(1\).
Complex multiplication
The elliptic curves in class 230640o do not have complex multiplication.Modular form 230640.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
