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SageMath
sage: E = EllipticCurve("cb1")
sage: E.isogeny_class()
Elliptic curves in class 88935.cb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 88935.cb1 | 88935s2 | \([0, -1, 1, -158839886, -14567227396723]\) | \(-2126464142970105856/438611057788643355\) | \(-91416360597662969163474158595\) | \([]\) | \(172800000\) | \(4.2364\) | |
| 88935.cb2 | 88935s1 | \([0, -1, 1, -53007236, 173973325217]\) | \(-79028701534867456/16987307596875\) | \(-3540535080644638438621875\) | \([]\) | \(34560000\) | \(3.4317\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 88935.cb have rank \(1\).
Complex multiplication
The elliptic curves in class 88935.cb do not have complex multiplication.Modular form 88935.2.a.cb
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
