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SageMath
E = EllipticCurve("ft1")
E.isogeny_class()
Elliptic curves in class 426888.ft
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
426888.ft1 | 426888ft1 | \([0, 0, 0, -35574, 2282665]\) | \(55296/7\) | \(630269277389136\) | \([2]\) | \(1658880\) | \(1.5690\) | \(\Gamma_0(N)\)-optimal |
426888.ft2 | 426888ft2 | \([0, 0, 0, 53361, 11869858]\) | \(11664/49\) | \(-70590159067583232\) | \([2]\) | \(3317760\) | \(1.9156\) |
Rank
sage: E.rank()
The elliptic curves in class 426888.ft have rank \(1\).
Complex multiplication
The elliptic curves in class 426888.ft do not have complex multiplication.Modular form 426888.2.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.