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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 309168.bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
309168.bb1 | 309168bb2 | \([0, 0, 0, -364183995, -1437542192662]\) | \(1788952473315990499029625/736296634487918297088\) | \(2198569969834772228412014592\) | \([]\) | \(116951040\) | \(3.9439\) | |
309168.bb2 | 309168bb1 | \([0, 0, 0, -168675915, 843121947386]\) | \(177744208950637895247625/17681950027579392\) | \(52798019871151623241728\) | \([]\) | \(38983680\) | \(3.3946\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 309168.bb have rank \(1\).
Complex multiplication
The elliptic curves in class 309168.bb do not have complex multiplication.Modular form 309168.2.a.bb
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.