Show commands:
SageMath
E = EllipticCurve("go1")
E.isogeny_class()
Elliptic curves in class 303450.go
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
303450.go1 | 303450go2 | \([1, 0, 0, -23653, -100303]\) | \(2383015010293/1372257936\) | \(842737904946000\) | \([2]\) | \(1622016\) | \(1.5536\) | |
303450.go2 | 303450go1 | \([1, 0, 0, -16853, -841503]\) | \(861985991413/2370816\) | \(1455977376000\) | \([2]\) | \(811008\) | \(1.2070\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 303450.go have rank \(1\).
Complex multiplication
The elliptic curves in class 303450.go do not have complex multiplication.Modular form 303450.2.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.