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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 139656q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 139656.q1 | 139656q1 | \([0, 1, 0, -4240640, 3359792304]\) | \(55635379958596/24057\) | \(3646770566833152\) | \([2]\) | \(3991680\) | \(2.3285\) | \(\Gamma_0(N)\)-optimal |
| 139656.q2 | 139656q2 | \([0, 1, 0, -4219480, 3395002544]\) | \(-27403349188178/578739249\) | \(-175460719052610275328\) | \([2]\) | \(7983360\) | \(2.6750\) |
Rank
sage: E.rank()
The elliptic curves in class 139656q have rank \(0\).
Complex multiplication
The elliptic curves in class 139656q do not have complex multiplication.Modular form 139656.2.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 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.
