Show commands:
SageMath
E = EllipticCurve("ch1")
E.isogeny_class()
Elliptic curves in class 4800ch
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4800.bm4 | 4800ch1 | \([0, 1, 0, 92, -3562]\) | \(85184/5625\) | \(-5625000000\) | \([2]\) | \(3072\) | \(0.55046\) | \(\Gamma_0(N)\)-optimal |
| 4800.bm3 | 4800ch2 | \([0, 1, 0, -3033, -62937]\) | \(48228544/2025\) | \(129600000000\) | \([2, 2]\) | \(6144\) | \(0.89704\) | |
| 4800.bm1 | 4800ch3 | \([0, 1, 0, -48033, -4067937]\) | \(23937672968/45\) | \(23040000000\) | \([2]\) | \(12288\) | \(1.2436\) | |
| 4800.bm2 | 4800ch4 | \([0, 1, 0, -8033, 192063]\) | \(111980168/32805\) | \(16796160000000\) | \([4]\) | \(12288\) | \(1.2436\) |
Rank
sage: E.rank()
The elliptic curves in class 4800ch have rank \(1\).
Complex multiplication
The elliptic curves in class 4800ch do not have complex multiplication.Modular form 4800.2.a.ch
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.
