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SageMath
E = EllipticCurve("ch1")
E.isogeny_class()
Elliptic curves in class 106560.ch
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 106560.ch1 | 106560eh1 | \([0, 0, 0, -30828, 2083408]\) | \(-16954786009/370\) | \(-70708101120\) | \([]\) | \(165888\) | \(1.1978\) | \(\Gamma_0(N)\)-optimal |
| 106560.ch2 | 106560eh2 | \([0, 0, 0, -10668, 4752592]\) | \(-702595369/50653000\) | \(-9679939043328000\) | \([]\) | \(497664\) | \(1.7471\) | |
| 106560.ch3 | 106560eh3 | \([0, 0, 0, 95892, -127424432]\) | \(510273943271/37000000000\) | \(-7070810112000000000\) | \([]\) | \(1492992\) | \(2.2964\) |
Rank
sage: E.rank()
The elliptic curves in class 106560.ch have rank \(1\).
Complex multiplication
The elliptic curves in class 106560.ch do not have complex multiplication.Modular form 106560.2.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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
