Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("ba1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3850.ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3850.ba1 3850o4 \([1, 1, 1, -391213, 72514531]\) \(423783056881319689/99207416000000\) \(1550115875000000000\) \([2]\) \(82944\) \(2.2022\)  
3850.ba2 3850o2 \([1, 1, 1, -365838, 85016531]\) \(346553430870203929/8300600\) \(129696875000\) \([2]\) \(27648\) \(1.6529\)  
3850.ba3 3850o1 \([1, 1, 1, -22838, 1324531]\) \(-84309998289049/414124480\) \(-6470695000000\) \([2]\) \(13824\) \(1.3064\) \(\Gamma_0(N)\)-optimal
3850.ba4 3850o3 \([1, 1, 1, 56787, 7106531]\) \(1296134247276791/2137096192000\) \(-33392128000000000\) \([2]\) \(41472\) \(1.8557\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 3850.2.a.ba

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.