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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 18480.bj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 18480.bj1 | 18480cf3 | \([0, -1, 0, -9200280, -10738056528]\) | \(21026497979043461623321/161783881875\) | \(662666780160000\) | \([2]\) | \(491520\) | \(2.4364\) | |
| 18480.bj2 | 18480cf2 | \([0, -1, 0, -575400, -167403600]\) | \(5143681768032498601/14238434358225\) | \(58320627131289600\) | \([2, 2]\) | \(245760\) | \(2.0899\) | |
| 18480.bj3 | 18480cf4 | \([0, -1, 0, -348600, -300943440]\) | \(-1143792273008057401/8897444448004035\) | \(-36443932459024527360\) | \([4]\) | \(491520\) | \(2.4364\) | |
| 18480.bj4 | 18480cf1 | \([0, -1, 0, -50520, -281808]\) | \(3481467828171481/2005331497785\) | \(8213837814927360\) | \([2]\) | \(122880\) | \(1.7433\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 18480.bj have rank \(0\).
Complex multiplication
The elliptic curves in class 18480.bj do not have complex multiplication.Modular form 18480.2.a.bj
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.
