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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 187200.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 187200.q1 | 187200cl4 | \([0, 0, 0, -1001100, -385526000]\) | \(37159393753/1053\) | \(3144241152000000\) | \([2]\) | \(2097152\) | \(2.0754\) | |
| 187200.q2 | 187200cl3 | \([0, 0, 0, -281100, 51946000]\) | \(822656953/85683\) | \(255848067072000000\) | \([2]\) | \(2097152\) | \(2.0754\) | |
| 187200.q3 | 187200cl2 | \([0, 0, 0, -65100, -5510000]\) | \(10218313/1521\) | \(4541681664000000\) | \([2, 2]\) | \(1048576\) | \(1.7288\) | |
| 187200.q4 | 187200cl1 | \([0, 0, 0, 6900, -470000]\) | \(12167/39\) | \(-116453376000000\) | \([2]\) | \(524288\) | \(1.3822\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 187200.q have rank \(2\).
Complex multiplication
The elliptic curves in class 187200.q do not have complex multiplication.Modular form 187200.2.a.q
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
