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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 234432bj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 234432.bj4 | 234432bj1 | \([0, 0, 0, -13125036, 15783832784]\) | \(1308451928740468777/194033737531392\) | \(37080424686651904622592\) | \([2]\) | \(23592960\) | \(3.0552\) | \(\Gamma_0(N)\)-optimal |
| 234432.bj2 | 234432bj2 | \([0, 0, 0, -201868716, 1103928896720]\) | \(4760617885089919932457/133756441657344\) | \(25561254059888810655744\) | \([2, 2]\) | \(47185920\) | \(3.4018\) | |
| 234432.bj1 | 234432bj3 | \([0, 0, 0, -3229877676, 70652449893584]\) | \(19499096390516434897995817/15393430272\) | \(2941730335827689472\) | \([2]\) | \(94371840\) | \(3.7483\) | |
| 234432.bj3 | 234432bj4 | \([0, 0, 0, -193758636, 1196691991760]\) | \(-4209586785160189454377/801182513521564416\) | \(-153108362653131200073302016\) | \([2]\) | \(94371840\) | \(3.7483\) |
Rank
sage: E.rank()
The elliptic curves in class 234432bj have rank \(1\).
Complex multiplication
The elliptic curves in class 234432bj do not have complex multiplication.Modular form 234432.2.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 Cremona 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 Cremona labels.
