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SageMath
E = EllipticCurve("ft1")
E.isogeny_class()
Elliptic curves in class 122304.ft
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
122304.ft1 | 122304dn2 | \([0, 1, 0, -2809, -46873]\) | \(5088448/1053\) | \(507430490112\) | \([2]\) | \(184320\) | \(0.96123\) | |
122304.ft2 | 122304dn1 | \([0, 1, 0, 376, -4194]\) | \(778688/1521\) | \(-11452424256\) | \([2]\) | \(92160\) | \(0.61466\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 122304.ft have rank \(1\).
Complex multiplication
The elliptic curves in class 122304.ft do not have complex multiplication.Modular form 122304.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.