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SageMath
E = EllipticCurve("ft1")
E.isogeny_class()
Elliptic curves in class 170352ft
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
170352.e1 | 170352ft1 | \([0, 0, 0, -132327, -18388890]\) | \(10536048/91\) | \(2213261675718912\) | \([2]\) | \(1806336\) | \(1.7688\) | \(\Gamma_0(N)\)-optimal |
170352.e2 | 170352ft2 | \([0, 0, 0, -41067, -43302870]\) | \(-78732/8281\) | \(-805627249961683968\) | \([2]\) | \(3612672\) | \(2.1154\) |
Rank
sage: E.rank()
The elliptic curves in class 170352ft have rank \(2\).
Complex multiplication
The elliptic curves in class 170352ft do not have complex multiplication.Modular form 170352.2.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 Cremona 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 Cremona labels.