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SageMath
E = EllipticCurve("iq1")
E.isogeny_class()
Elliptic curves in class 187200iq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 187200.bn2 | 187200iq1 | \([0, 0, 0, -128131500, 558249950000]\) | \(623295446073461/5458752\) | \(2037468266496000000000\) | \([2]\) | \(23592960\) | \(3.2557\) | \(\Gamma_0(N)\)-optimal |
| 187200.bn1 | 187200iq2 | \([0, 0, 0, -131011500, 531840350000]\) | \(666276475992821/58199166792\) | \(21722722606780416000000000\) | \([2]\) | \(47185920\) | \(3.6023\) |
Rank
sage: E.rank()
The elliptic curves in class 187200iq have rank \(0\).
Complex multiplication
The elliptic curves in class 187200iq do not have complex multiplication.Modular form 187200.2.a.iq
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.
