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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 166635n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
166635.n3 | 166635n1 | \([1, -1, 1, -12002, 482456]\) | \(1771561/105\) | \(11331407123505\) | \([2]\) | \(360448\) | \(1.2579\) | \(\Gamma_0(N)\)-optimal |
166635.n2 | 166635n2 | \([1, -1, 1, -35807, -2002786]\) | \(47045881/11025\) | \(1189797747968025\) | \([2, 2]\) | \(720896\) | \(1.6045\) | |
166635.n4 | 166635n3 | \([1, -1, 1, 83218, -12572206]\) | \(590589719/972405\) | \(-104940161370779805\) | \([2]\) | \(1441792\) | \(1.9511\) | |
166635.n1 | 166635n4 | \([1, -1, 1, -535712, -150774514]\) | \(157551496201/13125\) | \(1416425890438125\) | \([2]\) | \(1441792\) | \(1.9511\) |
Rank
sage: E.rank()
The elliptic curves in class 166635n have rank \(0\).
Complex multiplication
The elliptic curves in class 166635n do not have complex multiplication.Modular form 166635.2.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.