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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 880j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 880.j4 | 880j1 | \([0, -1, 0, -45, -100]\) | \(643956736/15125\) | \(242000\) | \([2]\) | \(144\) | \(-0.18143\) | \(\Gamma_0(N)\)-optimal |
| 880.j3 | 880j2 | \([0, -1, 0, -100, 252]\) | \(436334416/171875\) | \(44000000\) | \([2]\) | \(288\) | \(0.16514\) | |
| 880.j2 | 880j3 | \([0, -1, 0, -445, 3720]\) | \(610462990336/8857805\) | \(141724880\) | \([2]\) | \(432\) | \(0.36788\) | |
| 880.j1 | 880j4 | \([0, -1, 0, -7100, 232652]\) | \(154639330142416/33275\) | \(8518400\) | \([2]\) | \(864\) | \(0.71445\) |
Rank
sage: E.rank()
The elliptic curves in class 880j have rank \(0\).
Complex multiplication
The elliptic curves in class 880j do not have complex multiplication.Modular form 880.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
