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SageMath
E = EllipticCurve("ep1")
E.isogeny_class()
Elliptic curves in class 206400.ep
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
206400.ep1 | 206400dk2 | \([0, -1, 0, -181473, -24160383]\) | \(20170293914861/3938458752\) | \(129055416385536000\) | \([2]\) | \(2064384\) | \(2.0000\) | |
206400.ep2 | 206400dk1 | \([0, -1, 0, 23327, -2246783]\) | \(42838260499/90882048\) | \(-2978022948864000\) | \([2]\) | \(1032192\) | \(1.6535\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 206400.ep have rank \(0\).
Complex multiplication
The elliptic curves in class 206400.ep do not have complex multiplication.Modular form 206400.2.a.ep
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.