Show commands:
SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 10830o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10830.n2 | 10830o1 | \([1, 0, 1, -8, 19298]\) | \(-1/3420\) | \(-160896913020\) | \([2]\) | \(17280\) | \(0.82922\) | \(\Gamma_0(N)\)-optimal |
10830.n1 | 10830o2 | \([1, 0, 1, -10838, 426506]\) | \(2992209121/54150\) | \(2547534456150\) | \([2]\) | \(34560\) | \(1.1758\) |
Rank
sage: E.rank()
The elliptic curves in class 10830o have rank \(0\).
Complex multiplication
The elliptic curves in class 10830o do not have complex multiplication.Modular form 10830.2.a.o
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.