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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 69300k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 69300.cf2 | 69300k1 | \([0, 0, 0, 16200, -1636875]\) | \(95551488/290521\) | \(-1429581210750000\) | \([2]\) | \(230400\) | \(1.5913\) | \(\Gamma_0(N)\)-optimal |
| 69300.cf1 | 69300k2 | \([0, 0, 0, -149175, -19001250]\) | \(4662947952/717409\) | \(56483045388000000\) | \([2]\) | \(460800\) | \(1.9379\) |
Rank
sage: E.rank()
The elliptic curves in class 69300k have rank \(0\).
Complex multiplication
The elliptic curves in class 69300k do not have complex multiplication.Modular form 69300.2.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.
