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SageMath
E = EllipticCurve("cp1")
E.isogeny_class()
Elliptic curves in class 190575.cp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 190575.cp1 | 190575cm2 | \([0, 0, 1, -22905300, -42196069094]\) | \(-65860951343104/3493875\) | \(-70503557034216796875\) | \([]\) | \(9953280\) | \(2.8763\) | |
| 190575.cp2 | 190575cm1 | \([0, 0, 1, -36300, -154271219]\) | \(-262144/509355\) | \(-10278369802343671875\) | \([]\) | \(3317760\) | \(2.3270\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 190575.cp have rank \(2\).
Complex multiplication
The elliptic curves in class 190575.cp do not have complex multiplication.Modular form 190575.2.a.cp
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.
