Properties

Label 3850.j
Number of curves $4$
Conductor $3850$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3850.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3850.j1 3850c4 \([1, 1, 0, -88000, -10029750]\) \(4823468134087681/30382271150\) \(474722986718750\) \([2]\) \(27648\) \(1.6535\)  
3850.j2 3850c2 \([1, 1, 0, -6750, 201500]\) \(2177286259681/105875000\) \(1654296875000\) \([2]\) \(9216\) \(1.1042\)  
3850.j3 3850c3 \([1, 1, 0, -2250, -340000]\) \(-80677568161/3131816380\) \(-48934630937500\) \([2]\) \(13824\) \(1.3070\)  
3850.j4 3850c1 \([1, 1, 0, 250, 12500]\) \(109902239/4312000\) \(-67375000000\) \([2]\) \(4608\) \(0.75766\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 3850.j have rank \(1\).

Complex multiplication

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

Modular form 3850.2.a.j

sage: E.q_eigenform(10)
 
\(q - q^{2} + 2q^{3} + q^{4} - 2q^{6} - q^{7} - q^{8} + q^{9} - q^{11} + 2q^{12} - 2q^{13} + q^{14} + q^{16} - 6q^{17} - q^{18} + 2q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 3 & 2 & 6 \\ 3 & 1 & 6 & 2 \\ 2 & 6 & 1 & 3 \\ 6 & 2 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.