Show commands:
SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 381150.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
381150.o1 | 381150o2 | \([1, -1, 0, -5844867, -5437468459]\) | \(-4904170882875/43904\) | \(-197690658858000000\) | \([]\) | \(12192768\) | \(2.4844\) | |
381150.o2 | 381150o1 | \([1, -1, 0, -36867, -14732459]\) | \(-897199875/14680064\) | \(-90673938432000000\) | \([]\) | \(4064256\) | \(1.9351\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 381150.o have rank \(0\).
Complex multiplication
The elliptic curves in class 381150.o do not have complex multiplication.Modular form 381150.2.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.