Show commands:
SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 4800.u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4800.u1 | 4800bh3 | \([0, -1, 0, -5633, 163137]\) | \(38614472/405\) | \(207360000000\) | \([2]\) | \(6144\) | \(0.98802\) | |
| 4800.u2 | 4800bh2 | \([0, -1, 0, -633, -1863]\) | \(438976/225\) | \(14400000000\) | \([2, 2]\) | \(3072\) | \(0.64145\) | |
| 4800.u3 | 4800bh1 | \([0, -1, 0, -508, -4238]\) | \(14526784/15\) | \(15000000\) | \([2]\) | \(1536\) | \(0.29488\) | \(\Gamma_0(N)\)-optimal |
| 4800.u4 | 4800bh4 | \([0, -1, 0, 2367, -16863]\) | \(2863288/1875\) | \(-960000000000\) | \([2]\) | \(6144\) | \(0.98802\) |
Rank
sage: E.rank()
The elliptic curves in class 4800.u have rank \(0\).
Complex multiplication
The elliptic curves in class 4800.u do not have complex multiplication.Modular form 4800.2.a.u
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
