Properties

Label 3850.s
Number of curves $4$
Conductor $3850$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("s1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3850.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3850.s1 3850n3 \([1, -1, 1, -522730, -145336103]\) \(1010962818911303721/57392720\) \(896761250000\) \([2]\) \(24576\) \(1.7601\)  
3850.s2 3850n4 \([1, -1, 1, -54730, 1175897]\) \(1160306142246441/634128110000\) \(9908251718750000\) \([2]\) \(24576\) \(1.7601\)  
3850.s3 3850n2 \([1, -1, 1, -32730, -2256103]\) \(248158561089321/1859334400\) \(29052100000000\) \([2, 2]\) \(12288\) \(1.4135\)  
3850.s4 3850n1 \([1, -1, 1, -730, -80103]\) \(-2749884201/176619520\) \(-2759680000000\) \([4]\) \(6144\) \(1.0670\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 3850.s have rank \(0\).

Complex multiplication

The elliptic curves in class 3850.s do not have complex multiplication.

Modular form 3850.2.a.s

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{7} + q^{8} - 3q^{9} - q^{11} + 6q^{13} - q^{14} + q^{16} + 2q^{17} - 3q^{18} - 4q^{19} + O(q^{20})\)  Toggle raw display

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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.