Show commands:
SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 130536.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
130536.y1 | 130536bb2 | \([0, 0, 0, -181251, 28801710]\) | \(277706124/9583\) | \(22723800999588864\) | \([2]\) | \(737280\) | \(1.9101\) | |
130536.y2 | 130536bb1 | \([0, 0, 0, 3969, 1574370]\) | \(11664/1813\) | \(-1074774371602176\) | \([2]\) | \(368640\) | \(1.5635\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 130536.y have rank \(0\).
Complex multiplication
The elliptic curves in class 130536.y do not have complex multiplication.Modular form 130536.2.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.