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SageMath
E = EllipticCurve("ea1")
E.isogeny_class()
Elliptic curves in class 226512.ea
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 226512.ea1 | 226512by2 | \([0, 0, 0, -6308940, -6099338113]\) | \(11107182592000/13\) | \(32503665843792\) | \([]\) | \(3421440\) | \(2.3066\) | |
| 226512.ea2 | 226512by1 | \([0, 0, 0, -79860, -7920781]\) | \(22528000/2197\) | \(5493119527600848\) | \([]\) | \(1140480\) | \(1.7573\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 226512.ea have rank \(1\).
Complex multiplication
The elliptic curves in class 226512.ea do not have complex multiplication.Modular form 226512.2.a.ea
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
