Show commands:
SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 150590.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
150590.i1 | 150590r1 | \([1, 0, 1, -1398, 54816]\) | \(-117649/440\) | \(-1128919619960\) | \([]\) | \(204336\) | \(0.99835\) | \(\Gamma_0(N)\)-optimal |
150590.i2 | 150590r2 | \([1, 0, 1, 12292, -1303232]\) | \(80062991/332750\) | \(-853745462594750\) | \([]\) | \(613008\) | \(1.5477\) |
Rank
sage: E.rank()
The elliptic curves in class 150590.i have rank \(0\).
Complex multiplication
The elliptic curves in class 150590.i do not have complex multiplication.Modular form 150590.2.a.i
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.