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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 250470bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
250470.bb1 | 250470bb1 | \([1, -1, 0, -13422114360, -598517813869200]\) | \(275601091196478935659903044731/104123070000\) | \(101030510697930000\) | \([2]\) | \(154828800\) | \(4.0051\) | \(\Gamma_0(N)\)-optimal |
250470.bb2 | 250470bb2 | \([1, -1, 0, -13422112380, -598517999283924]\) | \(-275600969228345132090733365051/169400214159764062500\) | \(-164368858399004910079687500\) | \([2]\) | \(309657600\) | \(4.3517\) |
Rank
sage: E.rank()
The elliptic curves in class 250470bb have rank \(0\).
Complex multiplication
The elliptic curves in class 250470bb do not have complex multiplication.Modular form 250470.2.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 Cremona 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 Cremona labels.