Show commands:
SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 4800.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4800.f1 | 4800h3 | \([0, -1, 0, -3233, -69663]\) | \(7301384/3\) | \(1536000000\) | \([2]\) | \(4096\) | \(0.72507\) | |
| 4800.f2 | 4800h2 | \([0, -1, 0, -233, -663]\) | \(21952/9\) | \(576000000\) | \([2, 2]\) | \(2048\) | \(0.37850\) | |
| 4800.f3 | 4800h1 | \([0, -1, 0, -108, 462]\) | \(140608/3\) | \(3000000\) | \([2]\) | \(1024\) | \(0.031925\) | \(\Gamma_0(N)\)-optimal |
| 4800.f4 | 4800h4 | \([0, -1, 0, 767, -5663]\) | \(97336/81\) | \(-41472000000\) | \([2]\) | \(4096\) | \(0.72507\) |
Rank
sage: E.rank()
The elliptic curves in class 4800.f have rank \(1\).
Complex multiplication
The elliptic curves in class 4800.f do not have complex multiplication.Modular form 4800.2.a.f
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.
