Show commands:
SageMath
E = EllipticCurve("gw1")
E.isogeny_class()
Elliptic curves in class 336336.gw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
336336.gw1 | 336336gw1 | \([0, 1, 0, -4527130400, 117364955042292]\) | \(-21293376668673906679951249/26211168887701209984\) | \(-12630908143489677940357595136\) | \([]\) | \(320060160\) | \(4.3019\) | \(\Gamma_0(N)\)-optimal |
336336.gw2 | 336336gw2 | \([0, 1, 0, 12820821760, -7365865846182348]\) | \(483641001192506212470106511/48918776756543177755473774\) | \(-23573484202518725917711294616887296\) | \([]\) | \(2240421120\) | \(5.2749\) |
Rank
sage: E.rank()
The elliptic curves in class 336336.gw have rank \(1\).
Complex multiplication
The elliptic curves in class 336336.gw do not have complex multiplication.Modular form 336336.2.a.gw
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.