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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 490h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 490.h4 | 490h1 | \([1, -1, 1, 113, 711]\) | \(1367631/2800\) | \(-329417200\) | \([4]\) | \(192\) | \(0.31880\) | \(\Gamma_0(N)\)-optimal |
| 490.h3 | 490h2 | \([1, -1, 1, -867, 8159]\) | \(611960049/122500\) | \(14412002500\) | \([2, 2]\) | \(384\) | \(0.66537\) | |
| 490.h2 | 490h3 | \([1, -1, 1, -4297, -100229]\) | \(74565301329/5468750\) | \(643392968750\) | \([2]\) | \(768\) | \(1.0119\) | |
| 490.h1 | 490h4 | \([1, -1, 1, -13117, 581459]\) | \(2121328796049/120050\) | \(14123762450\) | \([2]\) | \(768\) | \(1.0119\) |
Rank
sage: E.rank()
The elliptic curves in class 490h have rank \(0\).
Complex multiplication
The elliptic curves in class 490h do not have complex multiplication.Modular form 490.2.a.h
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 Cremona 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 Cremona labels.
