Show commands:
SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 10608.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10608.g1 | 10608s2 | \([0, -1, 0, -4628, -119652]\) | \(42830942866000/146523\) | \(37509888\) | \([2]\) | \(7680\) | \(0.67381\) | |
10608.g2 | 10608s1 | \([0, -1, 0, -293, -1740]\) | \(174456832000/9771957\) | \(156351312\) | \([2]\) | \(3840\) | \(0.32724\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 10608.g have rank \(0\).
Complex multiplication
The elliptic curves in class 10608.g do not have complex multiplication.Modular form 10608.2.a.g
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.