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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 360789p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 360789.p4 | 360789p1 | \([1, 0, 1, 137065, -5689027]\) | \(478762350767/300661647\) | \(-178840559365869687\) | \([2]\) | \(3763200\) | \(1.9995\) | \(\Gamma_0(N)\)-optimal |
| 360789.p3 | 360789p2 | \([1, 0, 1, -573580, -46622179]\) | \(35084608539553/18728196201\) | \(11139967860618403521\) | \([2, 2]\) | \(7526400\) | \(2.3461\) | |
| 360789.p2 | 360789p3 | \([1, 0, 1, -5329435, 4699721111]\) | \(28143565473593233/242439894411\) | \(144208903136440358931\) | \([2]\) | \(15052800\) | \(2.6926\) | |
| 360789.p1 | 360789p4 | \([1, 0, 1, -7188045, -7409844617]\) | \(69050686357244593/90116794053\) | \(53603570716478510013\) | \([2]\) | \(15052800\) | \(2.6926\) |
Rank
sage: E.rank()
The elliptic curves in class 360789p have rank \(0\).
Complex multiplication
The elliptic curves in class 360789p do not have complex multiplication.Modular form 360789.2.a.p
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.
