Show commands:
SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 33856.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
33856.o1 | 33856k2 | \([0, -1, 0, -38793, 3607153]\) | \(-42592000/12167\) | \(-1844380325338112\) | \([]\) | \(101376\) | \(1.6444\) | |
33856.o2 | 33856k1 | \([0, -1, 0, 3527, -40831]\) | \(32000/23\) | \(-3486541257728\) | \([]\) | \(33792\) | \(1.0951\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 33856.o have rank \(0\).
Complex multiplication
The elliptic curves in class 33856.o do not have complex multiplication.Modular form 33856.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.