Show commands:
SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 10080.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10080.o1 | 10080o1 | \([0, 0, 0, -12333, -527168]\) | \(4446542056384/25725\) | \(1200225600\) | \([2]\) | \(15360\) | \(0.93250\) | \(\Gamma_0(N)\)-optimal |
10080.o2 | 10080o2 | \([0, 0, 0, -12108, -547328]\) | \(-65743598656/5294205\) | \(-15808411422720\) | \([2]\) | \(30720\) | \(1.2791\) |
Rank
sage: E.rank()
The elliptic curves in class 10080.o have rank \(0\).
Complex multiplication
The elliptic curves in class 10080.o do not have complex multiplication.Modular form 10080.2.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 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.