Show commands:
SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 1110.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1110.o1 | 1110o2 | \([1, 0, 0, -51, 135]\) | \(14688124849/123210\) | \(123210\) | \([2]\) | \(160\) | \(-0.19763\) | |
1110.o2 | 1110o1 | \([1, 0, 0, -1, 5]\) | \(-117649/11100\) | \(-11100\) | \([2]\) | \(80\) | \(-0.54420\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1110.o have rank \(0\).
Complex multiplication
The elliptic curves in class 1110.o do not have complex multiplication.Modular form 1110.2.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.