Show commands:
SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 62790h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
62790.g3 | 62790h1 | \([1, 1, 0, -532, -4736]\) | \(16700655633481/861478800\) | \(861478800\) | \([2]\) | \(36864\) | \(0.47221\) | \(\Gamma_0(N)\)-optimal |
62790.g2 | 62790h2 | \([1, 1, 0, -1512, 16236]\) | \(382672988497801/98564602500\) | \(98564602500\) | \([2, 2]\) | \(73728\) | \(0.81879\) | |
62790.g4 | 62790h3 | \([1, 1, 0, 3738, 109686]\) | \(5773777631458199/8392165741050\) | \(-8392165741050\) | \([2]\) | \(147456\) | \(1.1654\) | |
62790.g1 | 62790h4 | \([1, 1, 0, -22442, 1284594]\) | \(1250082349340708521/132447656250\) | \(132447656250\) | \([2]\) | \(147456\) | \(1.1654\) |
Rank
sage: E.rank()
The elliptic curves in class 62790h have rank \(1\).
Complex multiplication
The elliptic curves in class 62790h do not have complex multiplication.Modular form 62790.2.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.