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SageMath
E = EllipticCurve("mx1")
E.isogeny_class()
Elliptic curves in class 487872.mx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 487872.mx1 | 487872mx1 | \([0, 0, 0, -257004, 50109488]\) | \(598885164/539\) | \(1689618168741888\) | \([2]\) | \(3440640\) | \(1.8463\) | \(\Gamma_0(N)\)-optimal |
| 487872.mx2 | 487872mx2 | \([0, 0, 0, -198924, 73364720]\) | \(-138853062/290521\) | \(-1821408385903755264\) | \([2]\) | \(6881280\) | \(2.1929\) |
Rank
sage: E.rank()
The elliptic curves in class 487872.mx have rank \(0\).
Complex multiplication
The elliptic curves in class 487872.mx do not have complex multiplication.Modular form 487872.2.a.mx
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.
