Show commands:
SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 5390.x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5390.x1 | 5390be1 | \([1, 1, 1, -50, -393]\) | \(-117649/440\) | \(-51765560\) | \([]\) | \(1512\) | \(0.16585\) | \(\Gamma_0(N)\)-optimal |
5390.x2 | 5390be2 | \([1, 1, 1, 440, 9015]\) | \(80062991/332750\) | \(-39147704750\) | \([]\) | \(4536\) | \(0.71516\) |
Rank
sage: E.rank()
The elliptic curves in class 5390.x have rank \(0\).
Complex multiplication
The elliptic curves in class 5390.x do not have complex multiplication.Modular form 5390.2.a.x
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.