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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 333270.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
333270.p1 | 333270p2 | \([1, -1, 0, -21371400, -38260237464]\) | \(-2799235530137373837169/20348876953125000\) | \(-7847361257080078125000\) | \([]\) | \(24883200\) | \(3.0331\) | |
333270.p2 | 333270p1 | \([1, -1, 0, 761040, -279763200]\) | \(126404531110923791/160707758400000\) | \(-61975500657134400000\) | \([]\) | \(8294400\) | \(2.4838\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 333270.p have rank \(1\).
Complex multiplication
The elliptic curves in class 333270.p do not have complex multiplication.Modular form 333270.2.a.p
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.