Show commands:
SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 22050.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
22050.e1 | 22050s2 | \([1, -1, 0, -7947, 274511]\) | \(139798359/98\) | \(38912406750\) | \([2]\) | \(36864\) | \(0.96839\) | |
22050.e2 | 22050s1 | \([1, -1, 0, -597, 2561]\) | \(59319/28\) | \(11117830500\) | \([2]\) | \(18432\) | \(0.62182\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 22050.e have rank \(1\).
Complex multiplication
The elliptic curves in class 22050.e do not have complex multiplication.Modular form 22050.2.a.e
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.