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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 116610.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
116610.e1 | 116610a2 | \([1, 1, 0, -3796588, 55996192]\) | \(1253845972159670161/725308593750000\) | \(3500926048089843750000\) | \([2]\) | \(6193152\) | \(2.8234\) | |
116610.e2 | 116610a1 | \([1, 1, 0, 948932, 7591888]\) | \(19577992591125359/11334492000000\) | \(-54709427996028000000\) | \([2]\) | \(3096576\) | \(2.4768\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 116610.e have rank \(1\).
Complex multiplication
The elliptic curves in class 116610.e do not have complex multiplication.Modular form 116610.2.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.