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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 265650.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
265650.p1 | 265650p2 | \([1, 1, 0, -762143172325, -256096413909333875]\) | \(-3133382230165522315000208250857964625/153574604080128\) | \(-2399603188752000000\) | \([]\) | \(1293304320\) | \(4.9192\) | |
265650.p2 | 265650p1 | \([1, 1, 0, -9409092325, -351308200149875]\) | \(-5895856113332931416918127084625/215771481613620039647232\) | \(-3371429400212813119488000000\) | \([]\) | \(431101440\) | \(4.3699\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 265650.p have rank \(0\).
Complex multiplication
The elliptic curves in class 265650.p do not have complex multiplication.Modular form 265650.2.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.