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SageMath
E = EllipticCurve("fq1")
E.isogeny_class()
Elliptic curves in class 377520.fq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 377520.fq1 | 377520fq4 | \([0, 1, 0, -73855536, -244324055340]\) | \(6139836723518159689/3799803150\) | \(27572564247417446400\) | \([2]\) | \(35389440\) | \(3.0512\) | |
| 377520.fq2 | 377520fq3 | \([0, 1, 0, -10393456, 7413916244]\) | \(17111482619973769/6627044531250\) | \(48087915056438400000000\) | \([2]\) | \(35389440\) | \(3.0512\) | |
| 377520.fq3 | 377520fq2 | \([0, 1, 0, -4643536, -3770828140]\) | \(1525998818291689/37268302500\) | \(270430499820349440000\) | \([2, 2]\) | \(17694720\) | \(2.7046\) | |
| 377520.fq4 | 377520fq1 | \([0, 1, 0, 41584, -185774316]\) | \(1095912791/2055596400\) | \(-14916052639663718400\) | \([2]\) | \(8847360\) | \(2.3580\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 377520.fq have rank \(0\).
Complex multiplication
The elliptic curves in class 377520.fq do not have complex multiplication.Modular form 377520.2.a.fq
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
