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SageMath
E = EllipticCurve("eo1")
E.isogeny_class()
Elliptic curves in class 141120.eo
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 141120.eo1 | 141120me3 | \([0, 0, 0, -282828, 57892912]\) | \(890277128/15\) | \(42155763793920\) | \([2]\) | \(786432\) | \(1.7446\) | |
| 141120.eo2 | 141120me4 | \([0, 0, 0, -71148, -6415472]\) | \(14172488/1875\) | \(5269470474240000\) | \([2]\) | \(786432\) | \(1.7446\) | |
| 141120.eo3 | 141120me2 | \([0, 0, 0, -18228, 845152]\) | \(1906624/225\) | \(79042057113600\) | \([2, 2]\) | \(393216\) | \(1.3981\) | |
| 141120.eo4 | 141120me1 | \([0, 0, 0, 1617, 67228]\) | \(85184/405\) | \(-2223057856320\) | \([2]\) | \(196608\) | \(1.0515\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 141120.eo have rank \(1\).
Complex multiplication
The elliptic curves in class 141120.eo do not have complex multiplication.Modular form 141120.2.a.eo
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.
