Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 48510.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 48510.j1 | 48510r4 | \([1, -1, 0, -4656960450, -122320093527500]\) | \(130231365028993807856757649/4753980000\) | \(407730423911580000\) | \([2]\) | \(23592960\) | \(3.7975\) | |
| 48510.j2 | 48510r3 | \([1, -1, 0, -296493570, -1836128168204]\) | \(33608860073906150870929/2466782226562500000\) | \(211566342924008789062500000\) | \([2]\) | \(23592960\) | \(3.7975\) | |
| 48510.j3 | 48510r2 | \([1, -1, 0, -291060450, -1911191067500]\) | \(31794905164720991157649/192099600000000\) | \(16475637537651600000000\) | \([2, 2]\) | \(11796480\) | \(3.4509\) | |
| 48510.j4 | 48510r1 | \([1, -1, 0, -17852130, -31026050924]\) | \(-7336316844655213969/604492922880000\) | \(-51845013167369748480000\) | \([2]\) | \(5898240\) | \(3.1043\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 48510.j have rank \(1\).
Complex multiplication
The elliptic curves in class 48510.j do not have complex multiplication.Modular form 48510.2.a.j
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.
