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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 232562k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
232562.k2 | 232562k1 | \([1, 1, 1, 2863, -21185]\) | \(24167/16\) | \(-1718207126416\) | \([]\) | \(489600\) | \(1.0365\) | \(\Gamma_0(N)\)-optimal |
232562.k1 | 232562k2 | \([1, 1, 1, -49992, -4439863]\) | \(-128667913/4096\) | \(-439861024362496\) | \([]\) | \(1468800\) | \(1.5858\) |
Rank
sage: E.rank()
The elliptic curves in class 232562k have rank \(0\).
Complex multiplication
The elliptic curves in class 232562k do not have complex multiplication.Modular form 232562.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.