Show commands:
SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 59248.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
59248.y1 | 59248e2 | \([0, -1, 0, -544, -4560]\) | \(1431644/49\) | \(610491392\) | \([2]\) | \(21504\) | \(0.45770\) | |
59248.y2 | 59248e1 | \([0, -1, 0, -84, 224]\) | \(21296/7\) | \(21803264\) | \([2]\) | \(10752\) | \(0.11112\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 59248.y have rank \(0\).
Complex multiplication
The elliptic curves in class 59248.y do not have complex multiplication.Modular form 59248.2.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.