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SageMath
E = EllipticCurve("ko1")
E.isogeny_class()
Elliptic curves in class 95550.ko
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
95550.ko1 | 95550kp2 | \([1, 0, 0, -445803, 105530697]\) | \(666276475992821/58199166792\) | \(855884221739001000\) | \([2]\) | \(1769472\) | \(2.1815\) | |
95550.ko2 | 95550kp1 | \([1, 0, 0, -436003, 110773697]\) | \(623295446073461/5458752\) | \(80277089256000\) | \([2]\) | \(884736\) | \(1.8349\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 95550.ko have rank \(1\).
Complex multiplication
The elliptic curves in class 95550.ko do not have complex multiplication.Modular form 95550.2.a.ko
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.