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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 89232.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
89232.w1 | 89232bh1 | \([0, -1, 0, -15613980360, -751756082792976]\) | \(-21293376668673906679951249/26211168887701209984\) | \(-518210788915921672854163685376\) | \([]\) | \(142248960\) | \(4.6114\) | \(\Gamma_0(N)\)-optimal |
89232.w2 | 89232bh2 | \([0, -1, 0, 44218752600, 47180208739068144]\) | \(483641001192506212470106511/48918776756543177755473774\) | \(-967154040493971125365639625142951936\) | \([]\) | \(995742720\) | \(5.5844\) |
Rank
sage: E.rank()
The elliptic curves in class 89232.w have rank \(1\).
Complex multiplication
The elliptic curves in class 89232.w do not have complex multiplication.Modular form 89232.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.