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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 92950.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
92950.p1 | 92950c1 | \([1, 1, 0, -374000, 88720000]\) | \(-76711450249/851840\) | \(-64244827790000000\) | \([]\) | \(1548288\) | \(2.0400\) | \(\Gamma_0(N)\)-optimal |
92950.p2 | 92950c2 | \([1, 1, 0, 1252625, 461217125]\) | \(2882081488391/2883584000\) | \(-217476706304000000000\) | \([]\) | \(4644864\) | \(2.5893\) |
Rank
sage: E.rank()
The elliptic curves in class 92950.p have rank \(1\).
Complex multiplication
The elliptic curves in class 92950.p do not have complex multiplication.Modular form 92950.2.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.