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SageMath
E = EllipticCurve("go1")
E.isogeny_class()
Elliptic curves in class 73920.go
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 73920.go1 | 73920hh4 | \([0, 1, 0, -198385, -17998225]\) | \(52702650535889104/22020583921875\) | \(360785246976000000\) | \([2]\) | \(995328\) | \(2.0660\) | |
| 73920.go2 | 73920hh2 | \([0, 1, 0, -171025, -27280177]\) | \(33766427105425744/9823275\) | \(160944537600\) | \([2]\) | \(331776\) | \(1.5167\) | |
| 73920.go3 | 73920hh1 | \([0, 1, 0, -10645, -432565]\) | \(-130287139815424/2250652635\) | \(-2304668298240\) | \([2]\) | \(165888\) | \(1.1701\) | \(\Gamma_0(N)\)-optimal |
| 73920.go4 | 73920hh3 | \([0, 1, 0, 41195, -2042197]\) | \(7549996227362816/6152409907875\) | \(-6300067745664000\) | \([2]\) | \(497664\) | \(1.7194\) |
Rank
sage: E.rank()
The elliptic curves in class 73920.go have rank \(0\).
Complex multiplication
The elliptic curves in class 73920.go do not have complex multiplication.Modular form 73920.2.a.go
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.
