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SageMath
E = EllipticCurve("ft1")
E.isogeny_class()
Elliptic curves in class 103488ft
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 103488.eh1 | 103488ft1 | \([0, -1, 0, -1571201, -757522527]\) | \(55635379958596/24057\) | \(185485360693248\) | \([2]\) | \(1935360\) | \(2.0802\) | \(\Gamma_0(N)\)-optimal |
| 103488.eh2 | 103488ft2 | \([0, -1, 0, -1563361, -765464447]\) | \(-27403349188178/578739249\) | \(-8924442644394934272\) | \([2]\) | \(3870720\) | \(2.4268\) |
Rank
sage: E.rank()
The elliptic curves in class 103488ft have rank \(1\).
Complex multiplication
The elliptic curves in class 103488ft do not have complex multiplication.Modular form 103488.2.a.ft
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.
