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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 4830.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4830.e1 | 4830e1 | \([1, 1, 0, -119387, 15827229]\) | \(188191720927962271801/9422571110400\) | \(9422571110400\) | \([2]\) | \(27648\) | \(1.5604\) | \(\Gamma_0(N)\)-optimal |
4830.e2 | 4830e2 | \([1, 1, 0, -112987, 17607709]\) | \(-159520003524722950201/42335913815758080\) | \(-42335913815758080\) | \([2]\) | \(55296\) | \(1.9070\) |
Rank
sage: E.rank()
The elliptic curves in class 4830.e have rank \(0\).
Complex multiplication
The elliptic curves in class 4830.e do not have complex multiplication.Modular form 4830.2.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.