Show commands:
SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 487872a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
487872.a2 | 487872a1 | \([0, 0, 0, -28228332, 90157574320]\) | \(-7347774183121/6119866368\) | \(-2071884303914071907893248\) | \([2]\) | \(123863040\) | \(3.3637\) | \(\Gamma_0(N)\)-optimal* |
487872.a1 | 487872a2 | \([0, 0, 0, -518888172, 4548292880560]\) | \(45637459887836881/13417633152\) | \(4542547475982059644649472\) | \([2]\) | \(247726080\) | \(3.7103\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 487872a have rank \(1\).
Complex multiplication
The elliptic curves in class 487872a do not have complex multiplication.Modular form 487872.2.a.a
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.