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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 363090.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 363090.q1 | 363090q4 | \([1, 1, 0, -10701968, -13479919662]\) | \(1152196308890224287481/5336644950\) | \(627850941722550\) | \([2]\) | \(12582912\) | \(2.4644\) | |
| 363090.q2 | 363090q2 | \([1, 1, 0, -669218, -210604512]\) | \(281734042678323481/605361802500\) | \(71220210702322500\) | \([2, 2]\) | \(6291456\) | \(2.1178\) | |
| 363090.q3 | 363090q3 | \([1, 1, 0, -436468, -358959362]\) | \(-78161746041159481/427424303164950\) | \(-50286041843053202550\) | \([2]\) | \(12582912\) | \(2.4644\) | |
| 363090.q4 | 363090q1 | \([1, 1, 0, -56718, -762012]\) | \(171518180523481/97256250000\) | \(11442100556250000\) | \([2]\) | \(3145728\) | \(1.7713\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 363090.q have rank \(0\).
Complex multiplication
The elliptic curves in class 363090.q do not have complex multiplication.Modular form 363090.2.a.q
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.
