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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 2842.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2842.e1 | 2842e2 | \([1, 0, 0, -22296, 1288244]\) | \(-10418796526321/82044596\) | \(-9652464674804\) | \([]\) | \(7200\) | \(1.3201\) | |
2842.e2 | 2842e1 | \([1, 0, 0, 244, -2416]\) | \(13651919/29696\) | \(-3493704704\) | \([]\) | \(1440\) | \(0.51540\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2842.e have rank \(1\).
Complex multiplication
The elliptic curves in class 2842.e do not have complex multiplication.Modular form 2842.2.a.e
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.