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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 55506.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
55506.w1 | 55506s2 | \([1, 0, 1, -24150174, -45339549296]\) | \(2618764779527817409/22654590064128\) | \(13475478497838219929088\) | \([2]\) | \(8467200\) | \(3.0706\) | |
55506.w2 | 55506s1 | \([1, 0, 1, -467614, -1668908656]\) | \(-19010647320769/2011741028352\) | \(-1196630479476291796992\) | \([2]\) | \(4233600\) | \(2.7240\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 55506.w have rank \(1\).
Complex multiplication
The elliptic curves in class 55506.w do not have complex multiplication.Modular form 55506.2.a.w
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.