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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 81144.bd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
81144.bd1 | 81144bi2 | \([0, 0, 0, -7483035, 1148735126]\) | \(263822189935250/149429406721\) | \(26247128223316990445568\) | \([2]\) | \(4423680\) | \(2.9918\) | |
81144.bd2 | 81144bi1 | \([0, 0, 0, 1848525, 142792958]\) | \(7953970437500/4703287687\) | \(-413063926641717378048\) | \([2]\) | \(2211840\) | \(2.6452\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 81144.bd have rank \(0\).
Complex multiplication
The elliptic curves in class 81144.bd do not have complex multiplication.Modular form 81144.2.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.