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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 466578bl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
466578.bl2 | 466578bl1 | \([1, -1, 0, -2037807, 1131785325]\) | \(-25282750375/304704\) | \(-11278901915457527232\) | \([2]\) | \(9732096\) | \(2.4675\) | \(\Gamma_0(N)\)-optimal* |
466578.bl1 | 466578bl2 | \([1, -1, 0, -32698647, 71976722229]\) | \(104453838382375/14904\) | \(551685419777813832\) | \([2]\) | \(19464192\) | \(2.8140\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 466578bl have rank \(0\).
Complex multiplication
The elliptic curves in class 466578bl do not have complex multiplication.Modular form 466578.2.a.bl
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.