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SageMath
E = EllipticCurve("fq1")
E.isogeny_class()
Elliptic curves in class 152880fq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
152880.gk3 | 152880fq1 | \([0, 1, 0, -5455, 152900]\) | \(9538484224/26325\) | \(49553758800\) | \([2]\) | \(221184\) | \(0.92513\) | \(\Gamma_0(N)\)-optimal |
152880.gk2 | 152880fq2 | \([0, 1, 0, -7660, 15308]\) | \(1650587344/950625\) | \(28631060640000\) | \([2, 2]\) | \(442368\) | \(1.2717\) | |
152880.gk4 | 152880fq3 | \([0, 1, 0, 30560, 152900]\) | \(26198797244/15234375\) | \(-1835324400000000\) | \([2]\) | \(884736\) | \(1.6183\) | |
152880.gk1 | 152880fq4 | \([0, 1, 0, -81160, -8892892]\) | \(490757540836/2142075\) | \(258061293235200\) | \([2]\) | \(884736\) | \(1.6183\) |
Rank
sage: E.rank()
The elliptic curves in class 152880fq have rank \(0\).
Complex multiplication
The elliptic curves in class 152880fq do not have complex multiplication.Modular form 152880.2.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 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.