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SageMath
E = EllipticCurve("ch1")
E.isogeny_class()
Elliptic curves in class 76050.ch
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 76050.ch1 | 76050bh4 | \([1, -1, 0, -45478692, 112052593966]\) | \(189208196468929/10860320250\) | \(597104439408585316406250\) | \([2]\) | \(9289728\) | \(3.3163\) | |
| 76050.ch2 | 76050bh2 | \([1, -1, 0, -7833942, -8400339284]\) | \(967068262369/4928040\) | \(270945468811850625000\) | \([2]\) | \(3096576\) | \(2.7670\) | |
| 76050.ch3 | 76050bh1 | \([1, -1, 0, -228942, -270594284]\) | \(-24137569/561600\) | \(-30876976502775000000\) | \([2]\) | \(1548288\) | \(2.4204\) | \(\Gamma_0(N)\)-optimal |
| 76050.ch4 | 76050bh3 | \([1, -1, 0, 2052558, 7151125216]\) | \(17394111071/411937500\) | \(-22648476688233398437500\) | \([2]\) | \(4644864\) | \(2.9697\) |
Rank
sage: E.rank()
The elliptic curves in class 76050.ch have rank \(0\).
Complex multiplication
The elliptic curves in class 76050.ch do not have complex multiplication.Modular form 76050.2.a.ch
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
