Show commands:
SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 27225.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
27225.y1 | 27225bg1 | \([0, 0, 1, -25410, 1635466]\) | \(-56197120/3267\) | \(-105480646368075\) | \([]\) | \(69120\) | \(1.4470\) | \(\Gamma_0(N)\)-optimal |
27225.y2 | 27225bg2 | \([0, 0, 1, 137940, 2893261]\) | \(8990228480/5314683\) | \(-171593571497220675\) | \([]\) | \(207360\) | \(1.9963\) |
Rank
sage: E.rank()
The elliptic curves in class 27225.y have rank \(1\).
Complex multiplication
The elliptic curves in class 27225.y do not have complex multiplication.Modular form 27225.2.a.y
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.