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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 66240.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 66240.q1 | 66240e2 | \([0, 0, 0, -1084428, 422176752]\) | \(27333463470867/895491200\) | \(4620537899148902400\) | \([2]\) | \(1032192\) | \(2.3549\) | |
| 66240.q2 | 66240e1 | \([0, 0, 0, 21492, 22718448]\) | \(212776173/43335680\) | \(-223602590204559360\) | \([2]\) | \(516096\) | \(2.0083\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 66240.q have rank \(1\).
Complex multiplication
The elliptic curves in class 66240.q do not have complex multiplication.Modular form 66240.2.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.
