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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 86394.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
86394.i1 | 86394l4 | \([1, 1, 0, -614561, -185692899]\) | \(14489843500598257/6246072\) | \(11065297558392\) | \([2]\) | \(1105920\) | \(1.8455\) | |
86394.i2 | 86394l3 | \([1, 1, 0, -82161, 4757229]\) | \(34623662831857/14438442312\) | \(25578581300689032\) | \([2]\) | \(1105920\) | \(1.8455\) | |
86394.i3 | 86394l2 | \([1, 1, 0, -38601, -2883195]\) | \(3590714269297/73410624\) | \(130051398464064\) | \([2, 2]\) | \(552960\) | \(1.4989\) | |
86394.i4 | 86394l1 | \([1, 1, 0, 119, -134075]\) | \(103823/4386816\) | \(-7771512139776\) | \([2]\) | \(276480\) | \(1.1523\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 86394.i have rank \(1\).
Complex multiplication
The elliptic curves in class 86394.i do not have complex multiplication.Modular form 86394.2.a.i
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.