Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 125902.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
125902.j1 | 125902e2 | \([1, 1, 0, -67987, 1267725]\) | \(234770924809/130960928\) | \(19386917400744992\) | \([2]\) | \(2027520\) | \(1.8156\) | |
125902.j2 | 125902e1 | \([1, 1, 0, 16653, 167405]\) | \(3449795831/2071552\) | \(-306664041929728\) | \([2]\) | \(1013760\) | \(1.4690\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 125902.j have rank \(1\).
Complex multiplication
The elliptic curves in class 125902.j do not have complex multiplication.Modular form 125902.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.