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SageMath
E = EllipticCurve("cy1")
E.isogeny_class()
Elliptic curves in class 48400cy
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 48400.bh3 | 48400cy1 | \([0, -1, 0, -1008, -145088]\) | \(-25/2\) | \(-9070392320000\) | \([]\) | \(64800\) | \(1.1660\) | \(\Gamma_0(N)\)-optimal |
| 48400.bh1 | 48400cy2 | \([0, -1, 0, -243008, -46028288]\) | \(-349938025/8\) | \(-36281569280000\) | \([]\) | \(194400\) | \(1.7153\) | |
| 48400.bh2 | 48400cy3 | \([0, -1, 0, -146208, 25990912]\) | \(-121945/32\) | \(-90703923200000000\) | \([]\) | \(324000\) | \(1.9707\) | |
| 48400.bh4 | 48400cy4 | \([0, -1, 0, 1063792, -191809088]\) | \(46969655/32768\) | \(-92880817356800000000\) | \([]\) | \(972000\) | \(2.5200\) |
Rank
sage: E.rank()
The elliptic curves in class 48400cy have rank \(0\).
Complex multiplication
The elliptic curves in class 48400cy do not have complex multiplication.Modular form 48400.2.a.cy
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 5 & 15 \\ 3 & 1 & 15 & 5 \\ 5 & 15 & 1 & 3 \\ 15 & 5 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
