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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 27720j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 27720.t4 | 27720j1 | \([0, 0, 0, -423, -8262]\) | \(-44851536/132055\) | \(-24644632320\) | \([2]\) | \(16384\) | \(0.68090\) | \(\Gamma_0(N)\)-optimal |
| 27720.t3 | 27720j2 | \([0, 0, 0, -9243, -341658]\) | \(116986321764/148225\) | \(110649369600\) | \([2, 2]\) | \(32768\) | \(1.0275\) | |
| 27720.t2 | 27720j3 | \([0, 0, 0, -11763, -140562]\) | \(120564797922/64054375\) | \(95632669440000\) | \([2]\) | \(65536\) | \(1.3740\) | |
| 27720.t1 | 27720j4 | \([0, 0, 0, -147843, -21880098]\) | \(239369344910082/385\) | \(574801920\) | \([2]\) | \(65536\) | \(1.3740\) |
Rank
sage: E.rank()
The elliptic curves in class 27720j have rank \(0\).
Complex multiplication
The elliptic curves in class 27720j do not have complex multiplication.Modular form 27720.2.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.
