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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 3850n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3850.s4 | 3850n1 | \([1, -1, 1, -730, -80103]\) | \(-2749884201/176619520\) | \(-2759680000000\) | \([4]\) | \(6144\) | \(1.0670\) | \(\Gamma_0(N)\)-optimal |
| 3850.s3 | 3850n2 | \([1, -1, 1, -32730, -2256103]\) | \(248158561089321/1859334400\) | \(29052100000000\) | \([2, 2]\) | \(12288\) | \(1.4135\) | |
| 3850.s1 | 3850n3 | \([1, -1, 1, -522730, -145336103]\) | \(1010962818911303721/57392720\) | \(896761250000\) | \([2]\) | \(24576\) | \(1.7601\) | |
| 3850.s2 | 3850n4 | \([1, -1, 1, -54730, 1175897]\) | \(1160306142246441/634128110000\) | \(9908251718750000\) | \([2]\) | \(24576\) | \(1.7601\) |
Rank
sage: E.rank()
The elliptic curves in class 3850n have rank \(0\).
Complex multiplication
The elliptic curves in class 3850n do not have complex multiplication.Modular form 3850.2.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.
