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SageMath
E = EllipticCurve("eu1")
E.isogeny_class()
Elliptic curves in class 76230.eu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 76230.eu1 | 76230fa4 | \([1, -1, 1, -35927222, 82894417719]\) | \(3971101377248209009/56495958750\) | \(72962721103570278750\) | \([2]\) | \(5898240\) | \(2.9510\) | |
| 76230.eu2 | 76230fa2 | \([1, -1, 1, -2309792, 1217509791]\) | \(1055257664218129/115307784900\) | \(148916310774691868100\) | \([2, 2]\) | \(2949120\) | \(2.6045\) | |
| 76230.eu3 | 76230fa1 | \([1, -1, 1, -545612, -134557761]\) | \(13908844989649/1980372240\) | \(2557587314656780560\) | \([2]\) | \(1474560\) | \(2.2579\) | \(\Gamma_0(N)\)-optimal |
| 76230.eu4 | 76230fa3 | \([1, -1, 1, 3080758, 6051755031]\) | \(2503876820718671/13702874328990\) | \(-17696823279122953121310\) | \([2]\) | \(5898240\) | \(2.9510\) |
Rank
sage: E.rank()
The elliptic curves in class 76230.eu have rank \(0\).
Complex multiplication
The elliptic curves in class 76230.eu do not have complex multiplication.Modular form 76230.2.a.eu
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.
