Show commands:
SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 350.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 350.b1 | 350a3 | \([1, -1, 0, -6692, -209034]\) | \(2121328796049/120050\) | \(1875781250\) | \([2]\) | \(384\) | \(0.84371\) | |
| 350.b2 | 350a4 | \([1, -1, 0, -2192, 37466]\) | \(74565301329/5468750\) | \(85449218750\) | \([2]\) | \(384\) | \(0.84371\) | |
| 350.b3 | 350a2 | \([1, -1, 0, -442, -2784]\) | \(611960049/122500\) | \(1914062500\) | \([2, 2]\) | \(192\) | \(0.49713\) | |
| 350.b4 | 350a1 | \([1, -1, 0, 58, -284]\) | \(1367631/2800\) | \(-43750000\) | \([2]\) | \(96\) | \(0.15056\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 350.b have rank \(0\).
Complex multiplication
The elliptic curves in class 350.b do not have complex multiplication.Modular form 350.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
