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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 179560.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 179560.g1 | 179560e3 | \([0, 0, 0, -480323, 128125038]\) | \(132304644/5\) | \(463146916705280\) | \([2]\) | \(1203840\) | \(1.9001\) | |
| 179560.g2 | 179560e2 | \([0, 0, 0, -31423, 1804578]\) | \(148176/25\) | \(578933645881600\) | \([2, 2]\) | \(601920\) | \(1.5536\) | |
| 179560.g3 | 179560e1 | \([0, 0, 0, -8978, -300763]\) | \(55296/5\) | \(7236670573520\) | \([2]\) | \(300960\) | \(1.2070\) | \(\Gamma_0(N)\)-optimal |
| 179560.g4 | 179560e4 | \([0, 0, 0, 58357, 10225942]\) | \(237276/625\) | \(-57893364588160000\) | \([2]\) | \(1203840\) | \(1.9001\) |
Rank
sage: E.rank()
The elliptic curves in class 179560.g have rank \(1\).
Complex multiplication
The elliptic curves in class 179560.g do not have complex multiplication.Modular form 179560.2.a.g
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
