Show commands:
SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 99450.v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 99450.v1 | 99450v4 | \([1, -1, 0, -245592, -46782684]\) | \(143820170742457/5826444\) | \(66366838687500\) | \([2]\) | \(524288\) | \(1.7345\) | |
| 99450.v2 | 99450v3 | \([1, -1, 0, -74592, 7244316]\) | \(4029546653497/351790452\) | \(4007113117312500\) | \([2]\) | \(524288\) | \(1.7345\) | |
| 99450.v3 | 99450v2 | \([1, -1, 0, -16092, -653184]\) | \(40459583737/7033104\) | \(80111450250000\) | \([2, 2]\) | \(262144\) | \(1.3879\) | |
| 99450.v4 | 99450v1 | \([1, -1, 0, 1908, -59184]\) | \(67419143/169728\) | \(-1933308000000\) | \([2]\) | \(131072\) | \(1.0413\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 99450.v have rank \(1\).
Complex multiplication
The elliptic curves in class 99450.v do not have complex multiplication.Modular form 99450.2.a.v
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.
