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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 56550.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
56550.e1 | 56550m2 | \([1, 1, 0, -190196190, 1005700058100]\) | \(6087222010775063608821562589/26635924560536796930048\) | \(3329490570067099616256000\) | \([2]\) | \(16214016\) | \(3.5582\) | |
56550.e2 | 56550m1 | \([1, 1, 0, -17959390, -2057458700]\) | \(5124936415700503726537949/2951296190454901506048\) | \(368912023806862688256000\) | \([2]\) | \(8107008\) | \(3.2116\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 56550.e have rank \(0\).
Complex multiplication
The elliptic curves in class 56550.e do not have complex multiplication.Modular form 56550.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.