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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 33930n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 33930.i1 | 33930n1 | \([1, -1, 0, -775734, 263169908]\) | \(70816584854952849249/271407185920\) | \(197855838535680\) | \([2]\) | \(393216\) | \(1.9571\) | \(\Gamma_0(N)\)-optimal |
| 33930.i2 | 33930n2 | \([1, -1, 0, -764214, 271356020]\) | \(-67708231728434700129/4390589032710400\) | \(-3200739404845881600\) | \([2]\) | \(786432\) | \(2.3037\) |
Rank
sage: E.rank()
The elliptic curves in class 33930n have rank \(0\).
Complex multiplication
The elliptic curves in class 33930n do not have complex multiplication.Modular form 33930.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
