Show commands:
SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 2730.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2730.g1 | 2730g1 | \([1, 1, 0, -8127, 273861]\) | \(59374229431741561/1153923563520\) | \(1153923563520\) | \([2]\) | \(6720\) | \(1.1071\) | \(\Gamma_0(N)\)-optimal |
2730.g2 | 2730g2 | \([1, 1, 0, 193, 817989]\) | \(788632918919/288997521321600\) | \(-288997521321600\) | \([2]\) | \(13440\) | \(1.4537\) |
Rank
sage: E.rank()
The elliptic curves in class 2730.g have rank \(0\).
Complex multiplication
The elliptic curves in class 2730.g do not have complex multiplication.Modular form 2730.2.a.g
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.