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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 16562o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
16562.t2 | 16562o1 | \([1, 1, 0, 49514, 69725076]\) | \(68921/10816\) | \(-2106731323715881408\) | \([2]\) | \(338688\) | \(2.1953\) | \(\Gamma_0(N)\)-optimal |
16562.t1 | 16562o2 | \([1, 1, 0, -2269166, 1274974940]\) | \(6634074439/228488\) | \(44504699213497994744\) | \([2]\) | \(677376\) | \(2.5418\) |
Rank
sage: E.rank()
The elliptic curves in class 16562o have rank \(0\).
Complex multiplication
The elliptic curves in class 16562o do not have complex multiplication.Modular form 16562.2.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.