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SageMath
E = EllipticCurve("pp1")
E.isogeny_class()
Elliptic curves in class 235200pp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
235200.pp2 | 235200pp1 | \([0, 1, 0, -1633, -59137]\) | \(-2401/6\) | \(-1204224000000\) | \([]\) | \(322560\) | \(1.0060\) | \(\Gamma_0(N)\)-optimal |
235200.pp1 | 235200pp2 | \([0, 1, 0, -225633, 42724863]\) | \(-6329617441/279936\) | \(-56184274944000000\) | \([]\) | \(2257920\) | \(1.9789\) |
Rank
sage: E.rank()
The elliptic curves in class 235200pp have rank \(1\).
Complex multiplication
The elliptic curves in class 235200pp do not have complex multiplication.Modular form 235200.2.a.pp
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.