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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 91260x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 91260.z1 | 91260x1 | \([0, 0, 0, -109512, 13999284]\) | \(-5971968/25\) | \(-608038921900800\) | \([]\) | \(505440\) | \(1.6917\) | \(\Gamma_0(N)\)-optimal |
| 91260.z2 | 91260x2 | \([0, 0, 0, 255528, 73792836]\) | \(8429568/15625\) | \(-3420218935692000000\) | \([]\) | \(1516320\) | \(2.2411\) |
Rank
sage: E.rank()
The elliptic curves in class 91260x have rank \(0\).
Complex multiplication
The elliptic curves in class 91260x do not have complex multiplication.Modular form 91260.2.a.x
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
