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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 185150.o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 185150.o1 | 185150cc3 | \([1, -1, 0, -3540167, 2564557491]\) | \(2121328796049/120050\) | \(277682944913281250\) | \([2]\) | \(4866048\) | \(2.4115\) | |
| 185150.o2 | 185150cc4 | \([1, -1, 0, -1159667, -448891009]\) | \(74565301329/5468750\) | \(12649551062011718750\) | \([2]\) | \(4866048\) | \(2.4115\) | |
| 185150.o3 | 185150cc2 | \([1, -1, 0, -233917, 35276241]\) | \(611960049/122500\) | \(283349943789062500\) | \([2, 2]\) | \(2433024\) | \(2.0649\) | |
| 185150.o4 | 185150cc1 | \([1, -1, 0, 30583, 3271741]\) | \(1367631/2800\) | \(-6476570143750000\) | \([2]\) | \(1216512\) | \(1.7183\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 185150.o have rank \(0\).
Complex multiplication
The elliptic curves in class 185150.o do not have complex multiplication.Modular form 185150.2.a.o
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
