Show commands:
SageMath
E = EllipticCurve("by1")
E.isogeny_class()
Elliptic curves in class 19600by
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
19600.ed1 | 19600by1 | \([0, 0, 0, -2581075, -1596064750]\) | \(-5154200289/20\) | \(-7378945280000000\) | \([]\) | \(483840\) | \(2.2580\) | \(\Gamma_0(N)\)-optimal |
19600.ed2 | 19600by2 | \([0, 0, 0, 17998925, 15143707250]\) | \(1747829720511/1280000000\) | \(-472252497920000000000000\) | \([]\) | \(3386880\) | \(3.2310\) |
Rank
sage: E.rank()
The elliptic curves in class 19600by have rank \(0\).
Complex multiplication
The elliptic curves in class 19600by do not have complex multiplication.Modular form 19600.2.a.by
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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.