Show commands:
SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 2112.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2112.u1 | 2112bc2 | \([0, 1, 0, -49, 47]\) | \(810448/363\) | \(5947392\) | \([2]\) | \(384\) | \(-0.0047200\) | |
2112.u2 | 2112bc1 | \([0, 1, 0, 11, 11]\) | \(131072/99\) | \(-101376\) | \([2]\) | \(192\) | \(-0.35129\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2112.u have rank \(0\).
Complex multiplication
The elliptic curves in class 2112.u do not have complex multiplication.Modular form 2112.2.a.u
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.