Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3850.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3850.k1 3850d4 \([1, 1, 0, -652900, -197575500]\) \(1969902499564819009/63690429687500\) \(995162963867187500\) \([2]\) \(82944\) \(2.2274\)  
3850.k2 3850d2 \([1, 1, 0, -89400, 10160000]\) \(5057359576472449/51765560000\) \(808836875000000\) \([2]\) \(27648\) \(1.6781\)  
3850.k3 3850d1 \([1, 1, 0, -1400, 392000]\) \(-19443408769/4249907200\) \(-66404800000000\) \([2]\) \(13824\) \(1.3315\) \(\Gamma_0(N)\)-optimal
3850.k4 3850d3 \([1, 1, 0, 12600, -10570000]\) \(14156681599871/3100231750000\) \(-48441121093750000\) \([2]\) \(41472\) \(1.8808\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 3850.2.a.k

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.