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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 298816o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 298816.o2 | 298816o1 | \([0, 1, 0, -691415137, 7035013513983]\) | \(-139444195316122186685933977/867810592237096964848\) | \(-227491339891401546753114112\) | \([2]\) | \(139689984\) | \(3.8957\) | \(\Gamma_0(N)\)-optimal |
| 298816.o1 | 298816o2 | \([0, 1, 0, -11079113057, 448850814066175]\) | \(573718392227901342193352375257/22016176259779893044\) | \(5771408509443740282126336\) | \([2]\) | \(279379968\) | \(4.2423\) |
Rank
sage: E.rank()
The elliptic curves in class 298816o have rank \(1\).
Complex multiplication
The elliptic curves in class 298816o do not have complex multiplication.Modular form 298816.2.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.
