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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 960.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 960.d1 | 960j3 | \([0, -1, 0, -1921, -31775]\) | \(23937672968/45\) | \(1474560\) | \([2]\) | \(512\) | \(0.43889\) | |
| 960.d2 | 960j4 | \([0, -1, 0, -321, 1665]\) | \(111980168/32805\) | \(1074954240\) | \([2]\) | \(512\) | \(0.43889\) | |
| 960.d3 | 960j2 | \([0, -1, 0, -121, -455]\) | \(48228544/2025\) | \(8294400\) | \([2, 2]\) | \(256\) | \(0.092319\) | |
| 960.d4 | 960j1 | \([0, -1, 0, 4, -30]\) | \(85184/5625\) | \(-360000\) | \([2]\) | \(128\) | \(-0.25425\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 960.d have rank \(0\).
Complex multiplication
The elliptic curves in class 960.d do not have complex multiplication.Modular form 960.2.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.
