Properties

Label 1850.f
Number of curves $4$
Conductor $1850$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1850.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1850.f1 1850a3 \([1, 1, 0, -131875, -18487875]\) \(16232905099479601/4052240\) \(63316250000\) \([2]\) \(6912\) \(1.4482\)  
1850.f2 1850a4 \([1, 1, 0, -131375, -18634375]\) \(-16048965315233521/256572640900\) \(-4008947514062500\) \([2]\) \(13824\) \(1.7948\)  
1850.f3 1850a1 \([1, 1, 0, -1875, -17875]\) \(46694890801/18944000\) \(296000000000\) \([2]\) \(2304\) \(0.89892\) \(\Gamma_0(N)\)-optimal
1850.f4 1850a2 \([1, 1, 0, 6125, -121875]\) \(1625964918479/1369000000\) \(-21390625000000\) \([2]\) \(4608\) \(1.2455\)  

Rank

sage: E.rank()
 

The elliptic curves in class 1850.f have rank \(1\).

Complex multiplication

The elliptic curves in class 1850.f do not have complex multiplication.

Modular form 1850.2.a.f

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.