Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 214080.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
214080.j1 | 214080cu2 | \([0, -1, 0, -14480001, -30801412479]\) | \(-1280824409818832580001/822726139895701410\) | \(-215672721216818750423040\) | \([]\) | \(26869248\) | \(3.1786\) | |
214080.j2 | 214080cu1 | \([0, -1, 0, -435201, 123315201]\) | \(-34773983355859201/4877010000000\) | \(-1278478909440000000\) | \([]\) | \(3838464\) | \(2.2057\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 214080.j have rank \(1\).
Complex multiplication
The elliptic curves in class 214080.j do not have complex multiplication.Modular form 214080.2.a.j
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.