Show commands:
SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 48510.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
48510.o1 | 48510z1 | \([1, -1, 0, -450, 10156]\) | \(-117649/440\) | \(-37737093240\) | \([]\) | \(45360\) | \(0.71516\) | \(\Gamma_0(N)\)-optimal |
48510.o2 | 48510z2 | \([1, -1, 0, 3960, -239450]\) | \(80062991/332750\) | \(-28538676762750\) | \([]\) | \(136080\) | \(1.2645\) |
Rank
sage: E.rank()
The elliptic curves in class 48510.o have rank \(0\).
Complex multiplication
The elliptic curves in class 48510.o do not have complex multiplication.Modular form 48510.2.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.