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SageMath
E = EllipticCurve("fe1")
E.isogeny_class()
Elliptic curves in class 76230.fe
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
76230.fe1 | 76230dc1 | \([1, -1, 1, -286067, -58807889]\) | \(74246873427/16940\) | \(590691619661220\) | \([2]\) | \(737280\) | \(1.8261\) | \(\Gamma_0(N)\)-optimal |
76230.fe2 | 76230dc2 | \([1, -1, 1, -253397, -72777581]\) | \(-51603494067/35870450\) | \(-1250789504632633350\) | \([2]\) | \(1474560\) | \(2.1727\) |
Rank
sage: E.rank()
The elliptic curves in class 76230.fe have rank \(1\).
Complex multiplication
The elliptic curves in class 76230.fe do not have complex multiplication.Modular form 76230.2.a.fe
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.