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SageMath
E = EllipticCurve("ik1")
E.isogeny_class()
Elliptic curves in class 235200.ik
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
235200.ik1 | 235200ik2 | \([0, -1, 0, -105513, 13226697]\) | \(2156689088/81\) | \(4879139328000\) | \([2]\) | \(884736\) | \(1.5210\) | |
235200.ik2 | 235200ik1 | \([0, -1, 0, -6288, 228222]\) | \(-29218112/6561\) | \(-6175160712000\) | \([2]\) | \(442368\) | \(1.1745\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 235200.ik have rank \(0\).
Complex multiplication
The elliptic curves in class 235200.ik do not have complex multiplication.Modular form 235200.2.a.ik
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 LMFDB 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 LMFDB labels.