Show commands:
SageMath
E = EllipticCurve("gb1")
E.isogeny_class()
Elliptic curves in class 91728.gb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
91728.gb1 | 91728c1 | \([0, 0, 0, -4263, -106330]\) | \(10536048/91\) | \(74000279808\) | \([2]\) | \(172032\) | \(0.90999\) | \(\Gamma_0(N)\)-optimal |
91728.gb2 | 91728c2 | \([0, 0, 0, -1323, -250390]\) | \(-78732/8281\) | \(-26936101850112\) | \([2]\) | \(344064\) | \(1.2566\) |
Rank
sage: E.rank()
The elliptic curves in class 91728.gb have rank \(0\).
Complex multiplication
The elliptic curves in class 91728.gb do not have complex multiplication.Modular form 91728.2.a.gb
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.