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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 1680.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1680.n1 | 1680q1 | \([0, 1, 0, -4061, -67590]\) | \(463030539649024/149501953125\) | \(2392031250000\) | \([2]\) | \(3360\) | \(1.0787\) | \(\Gamma_0(N)\)-optimal |
| 1680.n2 | 1680q2 | \([0, 1, 0, 11564, -448840]\) | \(667990736021936/732392128125\) | \(-187492384800000\) | \([2]\) | \(6720\) | \(1.4253\) |
Rank
sage: E.rank()
The elliptic curves in class 1680.n have rank \(0\).
Complex multiplication
The elliptic curves in class 1680.n do not have complex multiplication.Modular form 1680.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
