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SageMath
E = EllipticCurve("ft1")
E.isogeny_class()
Elliptic curves in class 83790.ft
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
83790.ft1 | 83790fs4 | \([1, -1, 1, -426677, -107146119]\) | \(100162392144121/23457780\) | \(2011882797871380\) | \([2]\) | \(1179648\) | \(1.9269\) | |
83790.ft2 | 83790fs3 | \([1, -1, 1, -197357, 32866089]\) | \(9912050027641/311647500\) | \(26728797194347500\) | \([2]\) | \(1179648\) | \(1.9269\) | |
83790.ft3 | 83790fs2 | \([1, -1, 1, -29777, -1253199]\) | \(34043726521/11696400\) | \(1003154857664400\) | \([2, 2]\) | \(589824\) | \(1.5804\) | |
83790.ft4 | 83790fs1 | \([1, -1, 1, 5503, -138351]\) | \(214921799/218880\) | \(-18772488564480\) | \([2]\) | \(294912\) | \(1.2338\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 83790.ft have rank \(0\).
Complex multiplication
The elliptic curves in class 83790.ft do not have complex multiplication.Modular form 83790.2.a.ft
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.