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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 990.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 990.h1 | 990j3 | \([1, -1, 1, -14423, -663069]\) | \(455129268177961/4392300\) | \(3201986700\) | \([2]\) | \(2048\) | \(0.98530\) | |
| 990.h2 | 990j2 | \([1, -1, 1, -923, -9669]\) | \(119168121961/10890000\) | \(7938810000\) | \([2, 2]\) | \(1024\) | \(0.63873\) | |
| 990.h3 | 990j1 | \([1, -1, 1, -203, 987]\) | \(1263214441/211200\) | \(153964800\) | \([4]\) | \(512\) | \(0.29215\) | \(\Gamma_0(N)\)-optimal |
| 990.h4 | 990j4 | \([1, -1, 1, 1057, -46893]\) | \(179310732119/1392187500\) | \(-1014904687500\) | \([2]\) | \(2048\) | \(0.98530\) |
Rank
sage: E.rank()
The elliptic curves in class 990.h have rank \(1\).
Complex multiplication
The elliptic curves in class 990.h do not have complex multiplication.Modular form 990.2.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 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.
