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SageMath
E = EllipticCurve("ft1")
E.isogeny_class()
Elliptic curves in class 28224.ft
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
28224.ft1 | 28224dz2 | \([0, 0, 0, -53676, -4786992]\) | \(-67645179/8\) | \(-2022633897984\) | \([]\) | \(82944\) | \(1.3868\) | |
28224.ft2 | 28224dz1 | \([0, 0, 0, 84, -20272]\) | \(189/512\) | \(-177570054144\) | \([]\) | \(27648\) | \(0.83750\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 28224.ft have rank \(1\).
Complex multiplication
The elliptic curves in class 28224.ft do not have complex multiplication.Modular form 28224.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.