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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 44100.bd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
44100.bd1 | 44100bu1 | \([0, 0, 0, -58800, 2015125]\) | \(1048576/525\) | \(11256803381250000\) | \([2]\) | \(221184\) | \(1.7728\) | \(\Gamma_0(N)\)-optimal |
44100.bd2 | 44100bu2 | \([0, 0, 0, 216825, 15520750]\) | \(3286064/2205\) | \(-756457187220000000\) | \([2]\) | \(442368\) | \(2.1193\) |
Rank
sage: E.rank()
The elliptic curves in class 44100.bd have rank \(0\).
Complex multiplication
The elliptic curves in class 44100.bd do not have complex multiplication.Modular form 44100.2.a.bd
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.