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SageMath
E = EllipticCurve("cy1")
E.isogeny_class()
Elliptic curves in class 26950.cy
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
26950.cy1 | 26950cr1 | \([1, 0, 0, -108438, -13884508]\) | \(-76711450249/851840\) | \(-1565908190000000\) | \([]\) | \(157248\) | \(1.7305\) | \(\Gamma_0(N)\)-optimal |
26950.cy2 | 26950cr2 | \([1, 0, 0, 363187, -71894383]\) | \(2882081488391/2883584000\) | \(-5300793344000000000\) | \([]\) | \(471744\) | \(2.2798\) |
Rank
sage: E.rank()
The elliptic curves in class 26950.cy have rank \(0\).
Complex multiplication
The elliptic curves in class 26950.cy do not have complex multiplication.Modular form 26950.2.a.cy
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.