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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 152880.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 152880.q1 | 152880fd2 | \([0, -1, 0, -315336821, 3129203517945]\) | \(-2349759874143293538304/1506328582763671875\) | \(-2223023237182617187500000000\) | \([]\) | \(64774080\) | \(3.9487\) | |
| 152880.q2 | 152880fd1 | \([0, -1, 0, 31395019, -61890961719]\) | \(2318898093666861056/2462855365546875\) | \(-3634654994984957580000000\) | \([]\) | \(21591360\) | \(3.3994\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 152880.q have rank \(1\).
Complex multiplication
The elliptic curves in class 152880.q do not have complex multiplication.Modular form 152880.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
