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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 116160.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 116160.d1 | 116160ga4 | \([0, -1, 0, -232481, 43222401]\) | \(23937672968/45\) | \(2612272988160\) | \([2]\) | \(737280\) | \(1.6378\) | |
| 116160.d2 | 116160ga3 | \([0, -1, 0, -38881, -2060639]\) | \(111980168/32805\) | \(1904347008368640\) | \([2]\) | \(737280\) | \(1.6378\) | |
| 116160.d3 | 116160ga2 | \([0, -1, 0, -14681, 664281]\) | \(48228544/2025\) | \(14694035558400\) | \([2, 2]\) | \(368640\) | \(1.2913\) | |
| 116160.d4 | 116160ga1 | \([0, -1, 0, 444, 38106]\) | \(85184/5625\) | \(-637761960000\) | \([2]\) | \(184320\) | \(0.94469\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 116160.d have rank \(1\).
Complex multiplication
The elliptic curves in class 116160.d do not have complex multiplication.Modular form 116160.2.a.d
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.
