Show commands:
SageMath
E = EllipticCurve("bz1")
E.isogeny_class()
Elliptic curves in class 486720bz
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
486720.bz2 | 486720bz1 | \([0, 0, 0, -427908, -178712768]\) | \(-601211584/609375\) | \(-8782784427456000000\) | \([2]\) | \(10321920\) | \(2.3305\) | \(\Gamma_0(N)\)-optimal* |
486720.bz1 | 486720bz2 | \([0, 0, 0, -8032908, -8760194768]\) | \(497169541448/190125\) | \(21921829930930176000\) | \([2]\) | \(20643840\) | \(2.6771\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 486720bz have rank \(1\).
Complex multiplication
The elliptic curves in class 486720bz do not have complex multiplication.Modular form 486720.2.a.bz
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.