Show commands:
SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 96600b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
96600.i4 | 96600b1 | \([0, -1, 0, -32908, -186188]\) | \(985329269584/566015625\) | \(2264062500000000\) | \([2]\) | \(393216\) | \(1.6360\) | \(\Gamma_0(N)\)-optimal |
96600.i2 | 96600b2 | \([0, -1, 0, -345408, 77938812]\) | \(284840777767396/1312250625\) | \(20996010000000000\) | \([2, 2]\) | \(786432\) | \(1.9825\) | |
96600.i3 | 96600b3 | \([0, -1, 0, -170408, 156688812]\) | \(-17101973157698/321306440175\) | \(-10281806085600000000\) | \([2]\) | \(1572864\) | \(2.3291\) | |
96600.i1 | 96600b4 | \([0, -1, 0, -5520408, 4994188812]\) | \(581416486276209698/12425175\) | \(397605600000000\) | \([2]\) | \(1572864\) | \(2.3291\) |
Rank
sage: E.rank()
The elliptic curves in class 96600b have rank \(0\).
Complex multiplication
The elliptic curves in class 96600b do not have complex multiplication.Modular form 96600.2.a.b
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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.