Show commands:
SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 2772b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2772.a2 | 2772b1 | \([0, 0, 0, 648, -13095]\) | \(95551488/290521\) | \(-91493197488\) | \([2]\) | \(2880\) | \(0.78661\) | \(\Gamma_0(N)\)-optimal |
2772.a1 | 2772b2 | \([0, 0, 0, -5967, -152010]\) | \(4662947952/717409\) | \(3614914904832\) | \([2]\) | \(5760\) | \(1.1332\) |
Rank
sage: E.rank()
The elliptic curves in class 2772b have rank \(1\).
Complex multiplication
The elliptic curves in class 2772b do not have complex multiplication.Modular form 2772.2.a.b
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 Cremona 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 Cremona labels.