Show commands:
SageMath
E = EllipticCurve("go1")
E.isogeny_class()
Elliptic curves in class 170352.go
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
170352.go1 | 170352gn1 | \([0, 0, 0, -14703, 681070]\) | \(10536048/91\) | \(3036024246528\) | \([2]\) | \(602112\) | \(1.2195\) | \(\Gamma_0(N)\)-optimal |
170352.go2 | 170352gn2 | \([0, 0, 0, -4563, 1603810]\) | \(-78732/8281\) | \(-1105112825736192\) | \([2]\) | \(1204224\) | \(1.5661\) |
Rank
sage: E.rank()
The elliptic curves in class 170352.go have rank \(0\).
Complex multiplication
The elliptic curves in class 170352.go do not have complex multiplication.Modular form 170352.2.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.