Show commands:
SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 2772.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2772.m1 | 2772a2 | \([0, 0, 0, -663, 5630]\) | \(4662947952/717409\) | \(4958731008\) | \([2]\) | \(1920\) | \(0.58388\) | |
| 2772.m2 | 2772a1 | \([0, 0, 0, 72, 485]\) | \(95551488/290521\) | \(-125505072\) | \([2]\) | \(960\) | \(0.23731\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2772.m have rank \(0\).
Complex multiplication
The elliptic curves in class 2772.m do not have complex multiplication.Modular form 2772.2.a.m
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.
