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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 97020.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 97020.q1 | 97020ca2 | \([0, 0, 0, -4884663, 4155261838]\) | \(1711503051568/7425\) | \(55917315279302400\) | \([2]\) | \(1806336\) | \(2.4204\) | |
| 97020.q2 | 97020ca1 | \([0, 0, 0, -300468, 67076737]\) | \(-6373654528/441045\) | \(-207593032974410160\) | \([2]\) | \(903168\) | \(2.0738\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 97020.q have rank \(1\).
Complex multiplication
The elliptic curves in class 97020.q do not have complex multiplication.Modular form 97020.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
