Show commands:
SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 57222.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
57222.y1 | 57222g2 | \([1, -1, 0, -473436, -125259098]\) | \(666940371553/37026\) | \(651520152119826\) | \([2]\) | \(442368\) | \(1.9079\) | |
57222.y2 | 57222g1 | \([1, -1, 0, -31266, -1716800]\) | \(192100033/38148\) | \(671263187032548\) | \([2]\) | \(221184\) | \(1.5613\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 57222.y have rank \(0\).
Complex multiplication
The elliptic curves in class 57222.y do not have complex multiplication.Modular form 57222.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.