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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 115920.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 115920.g1 | 115920p4 | \([0, 0, 0, -1669323, -830154022]\) | \(344577854816148242/2716875\) | \(4056272640000\) | \([2]\) | \(983040\) | \(2.0102\) | |
| 115920.g2 | 115920p2 | \([0, 0, 0, -104403, -12952798]\) | \(168591300897604/472410225\) | \(352652343321600\) | \([2, 2]\) | \(491520\) | \(1.6636\) | |
| 115920.g3 | 115920p3 | \([0, 0, 0, -63003, -23327638]\) | \(-18524646126002/146738831715\) | \(-219079901839841280\) | \([2]\) | \(983040\) | \(2.0102\) | |
| 115920.g4 | 115920p1 | \([0, 0, 0, -9183, -21922]\) | \(458891455696/264449745\) | \(49352669210880\) | \([2]\) | \(245760\) | \(1.3171\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 115920.g have rank \(0\).
Complex multiplication
The elliptic curves in class 115920.g do not have complex multiplication.Modular form 115920.2.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.
