Show commands:
SageMath
E = EllipticCurve("gd1")
E.isogeny_class()
Elliptic curves in class 486720.gd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
486720.gd1 | 486720gd2 | \([0, 0, 0, -1218828, -510020368]\) | \(434163602/7605\) | \(3507492788948828160\) | \([2]\) | \(8257536\) | \(2.3550\) | \(\Gamma_0(N)\)-optimal* |
486720.gd2 | 486720gd1 | \([0, 0, 0, -2028, -22813648]\) | \(-4/975\) | \(-224839281342873600\) | \([2]\) | \(4128768\) | \(2.0084\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 486720.gd have rank \(0\).
Complex multiplication
The elliptic curves in class 486720.gd do not have complex multiplication.Modular form 486720.2.a.gd
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.