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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 41070bd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
41070.bc2 | 41070bd1 | \([1, 0, 0, 112914, 2510460]\) | \(45326591/27000\) | \(-94836945255867000\) | \([3]\) | \(479520\) | \(1.9469\) | \(\Gamma_0(N)\)-optimal |
41070.bc1 | 41070bd2 | \([1, 0, 0, -1406676, -712608594]\) | \(-87637942369/11718750\) | \(-41161868600636718750\) | \([]\) | \(1438560\) | \(2.4962\) |
Rank
sage: E.rank()
The elliptic curves in class 41070bd have rank \(1\).
Complex multiplication
The elliptic curves in class 41070bd do not have complex multiplication.Modular form 41070.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.