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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 53550.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
53550.e1 | 53550m2 | \([1, -1, 0, -603563367, -5700542067459]\) | \(461103615103087102895631/619571373437190272\) | \(32672709146101830750000000\) | \([2]\) | \(23654400\) | \(3.8013\) | |
53550.e2 | 53550m1 | \([1, -1, 0, -27323367, -139249827459]\) | \(-42779190704491347471/134106202987839488\) | \(-7072006798186848000000000\) | \([2]\) | \(11827200\) | \(3.4547\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 53550.e have rank \(0\).
Complex multiplication
The elliptic curves in class 53550.e do not have complex multiplication.Modular form 53550.2.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.