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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 22736k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 22736.bh1 | 22736k1 | \([0, -1, 0, -359, -706]\) | \(2725888/1421\) | \(2674867664\) | \([2]\) | \(10752\) | \(0.50078\) | \(\Gamma_0(N)\)-optimal |
| 22736.bh2 | 22736k2 | \([0, -1, 0, 1356, -6880]\) | \(9148592/5887\) | \(-177305513728\) | \([2]\) | \(21504\) | \(0.84736\) |
Rank
sage: E.rank()
The elliptic curves in class 22736k have rank \(0\).
Complex multiplication
The elliptic curves in class 22736k do not have complex multiplication.Modular form 22736.2.a.k
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.
