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SageMath
E = EllipticCurve("fi1")
E.isogeny_class()
Elliptic curves in class 58800.fi
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
58800.fi1 | 58800kh2 | \([0, 1, 0, -57410208, -167448566412]\) | \(266916252066900625/162\) | \(12700800000000\) | \([]\) | \(3110400\) | \(2.7371\) | |
58800.fi2 | 58800kh1 | \([0, 1, 0, -710208, -228926412]\) | \(505318200625/4251528\) | \(333319795200000000\) | \([]\) | \(1036800\) | \(2.1878\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 58800.fi have rank \(1\).
Complex multiplication
The elliptic curves in class 58800.fi do not have complex multiplication.Modular form 58800.2.a.fi
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.