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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 16575h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 16575.j3 | 16575h1 | \([1, 0, 1, -651, 6073]\) | \(1948441249/89505\) | \(1398515625\) | \([2]\) | \(10752\) | \(0.51653\) | \(\Gamma_0(N)\)-optimal |
| 16575.j2 | 16575h2 | \([1, 0, 1, -1776, -20927]\) | \(39616946929/10989225\) | \(171706640625\) | \([2, 2]\) | \(21504\) | \(0.86310\) | |
| 16575.j1 | 16575h3 | \([1, 0, 1, -26151, -1629677]\) | \(126574061279329/16286595\) | \(254478046875\) | \([2]\) | \(43008\) | \(1.2097\) | |
| 16575.j4 | 16575h4 | \([1, 0, 1, 4599, -135677]\) | \(688699320191/910381875\) | \(-14224716796875\) | \([2]\) | \(43008\) | \(1.2097\) |
Rank
sage: E.rank()
The elliptic curves in class 16575h have rank \(1\).
Complex multiplication
The elliptic curves in class 16575h do not have complex multiplication.Modular form 16575.2.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.
