Show commands:
SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 53900.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
53900.y1 | 53900j2 | \([0, 1, 0, -94733, 11255663]\) | \(-199794688/1331\) | \(-626363276000000\) | \([]\) | \(233280\) | \(1.6747\) | |
53900.y2 | 53900j1 | \([0, 1, 0, 3267, 83663]\) | \(8192/11\) | \(-5176556000000\) | \([]\) | \(77760\) | \(1.1254\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 53900.y have rank \(1\).
Complex multiplication
The elliptic curves in class 53900.y do not have complex multiplication.Modular form 53900.2.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.