Show commands:
SageMath
E = EllipticCurve("go1")
E.isogeny_class()
Elliptic curves in class 288990.go
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
288990.go1 | 288990go2 | \([1, -1, 1, -45662, 3707799]\) | \(2992209121/54150\) | \(190539974658150\) | \([2]\) | \(1474560\) | \(1.5354\) | |
288990.go2 | 288990go1 | \([1, -1, 1, -32, 166911]\) | \(-1/3420\) | \(-12034103662620\) | \([2]\) | \(737280\) | \(1.1888\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 288990.go have rank \(0\).
Complex multiplication
The elliptic curves in class 288990.go do not have complex multiplication.Modular form 288990.2.a.go
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.