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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 185130.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 185130.n1 | 185130ee3 | \([1, -1, 0, -618494850, 5920570738660]\) | \(20260414982443110947641/720358602480\) | \(930320061296523963120\) | \([2]\) | \(35389440\) | \(3.5193\) | |
| 185130.n2 | 185130ee2 | \([1, -1, 0, -38711250, 92238121300]\) | \(4967657717692586041/29490113030400\) | \(38085536380951123257600\) | \([2, 2]\) | \(17694720\) | \(3.1727\) | |
| 185130.n3 | 185130ee4 | \([1, -1, 0, -16495650, 197349011140]\) | \(-384369029857072441/12804787777021680\) | \(-16536973263866213938567920\) | \([2]\) | \(35389440\) | \(3.5193\) | |
| 185130.n4 | 185130ee1 | \([1, -1, 0, -3863250, -478467500]\) | \(4937402992298041/2780405760000\) | \(3590804979863101440000\) | \([2]\) | \(8847360\) | \(2.8261\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 185130.n have rank \(1\).
Complex multiplication
The elliptic curves in class 185130.n do not have complex multiplication.Modular form 185130.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
