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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 18928j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 18928.o4 | 18928j1 | \([0, 0, 0, 2342509, -936708526]\) | \(71903073502287/60782804992\) | \(-1201713111779862642688\) | \([2]\) | \(725760\) | \(2.7325\) | \(\Gamma_0(N)\)-optimal |
| 18928.o3 | 18928j2 | \([0, 0, 0, -11501971, -8243825070]\) | \(8511781274893233/3440817243136\) | \(68027054639202439266304\) | \([2, 2]\) | \(1451520\) | \(3.0791\) | |
| 18928.o1 | 18928j3 | \([0, 0, 0, -159897491, -777971387310]\) | \(22868021811807457713/8953460393696\) | \(177015370585847382278144\) | \([2]\) | \(2903040\) | \(3.4256\) | |
| 18928.o2 | 18928j4 | \([0, 0, 0, -84618131, 293828278354]\) | \(3389174547561866673/74853681183008\) | \(1479902912582752917389312\) | \([2]\) | \(2903040\) | \(3.4256\) |
Rank
sage: E.rank()
The elliptic curves in class 18928j have rank \(0\).
Complex multiplication
The elliptic curves in class 18928j do not have complex multiplication.Modular form 18928.2.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 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.
