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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 134862n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 134862.bw3 | 134862n1 | \([1, 0, 0, -27297, -1017927]\) | \(466025146777/177366672\) | \(856115048709648\) | \([2]\) | \(737280\) | \(1.5646\) | \(\Gamma_0(N)\)-optimal |
| 134862.bw2 | 134862n2 | \([1, 0, 0, -192917, 31874205]\) | \(164503536215257/4178071044\) | \(20166750917818596\) | \([2, 2]\) | \(1474560\) | \(1.9112\) | |
| 134862.bw1 | 134862n3 | \([1, 0, 0, -3067607, 2067729663]\) | \(661397832743623417/443352042\) | \(2139975626493978\) | \([2]\) | \(2949120\) | \(2.2578\) | |
| 134862.bw4 | 134862n4 | \([1, 0, 0, 31853, 101777675]\) | \(740480746823/927484650666\) | \(-4476791259196504794\) | \([2]\) | \(2949120\) | \(2.2578\) |
Rank
sage: E.rank()
The elliptic curves in class 134862n have rank \(0\).
Complex multiplication
The elliptic curves in class 134862n do not have complex multiplication.Modular form 134862.2.a.n
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.
