Show commands:
SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 3150.be
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3150.be1 | 3150bo1 | \([1, -1, 1, -1535, -22633]\) | \(4386781853/27216\) | \(2480058000\) | \([2]\) | \(2560\) | \(0.64065\) | \(\Gamma_0(N)\)-optimal |
3150.be2 | 3150bo2 | \([1, -1, 1, -635, -49633]\) | \(-310288733/11573604\) | \(-1054644664500\) | \([2]\) | \(5120\) | \(0.98723\) |
Rank
sage: E.rank()
The elliptic curves in class 3150.be have rank \(0\).
Complex multiplication
The elliptic curves in class 3150.be do not have complex multiplication.Modular form 3150.2.a.be
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.