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Properties

Label 195195.c
Number of curves $4$
Conductor $195195$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 195195.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
195195.c1 195195q4 \([1, 1, 1, -60286106, -180191586502]\) \(5020133855441875347241/979263285\) \(4726716837407565\) \([2]\) \(11354112\) \(2.8393\)  
195195.c2 195195q3 \([1, 1, 1, -4372456, -1853231242]\) \(1915313845414200841/801618148245915\) \(3869257692516716735235\) \([2]\) \(11354112\) \(2.8393\)  
195195.c3 195195q2 \([1, 1, 1, -3768281, -2816044522]\) \(1226008404186998041/541305990225\) \(2612780625371942025\) \([2, 2]\) \(5677056\) \(2.4927\)  
195195.c4 195195q1 \([1, 1, 1, -198156, -58479972]\) \(-178272935636041/202051224375\) \(-975262668274269375\) \([2]\) \(2838528\) \(2.1462\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 195195.c have rank \(1\).

Complex multiplication

The elliptic curves in class 195195.c do not have complex multiplication.

Modular form 195195.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} - q^{4} - q^{5} + q^{6} - q^{7} + 3 q^{8} + q^{9} + q^{10} - q^{11} + q^{12} + q^{14} + q^{15} - q^{16} + 6 q^{17} - q^{18} - 4 q^{19} + O(q^{20})\) Copy content 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.