Properties

Label 47190.cq
Number of curves $2$
Conductor $47190$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("cq1")
 
E.isogeny_class()
 

Elliptic curves in class 47190.cq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47190.cq1 47190cl2 \([1, 0, 0, -2868841, 1877251025]\) \(-21580315425730848803929/96405029296875000\) \(-11665008544921875000\) \([]\) \(2332800\) \(2.5108\)  
47190.cq2 47190cl1 \([1, 0, 0, 84824, 13627406]\) \(557820238477845431/985142146218750\) \(-119202199692468750\) \([]\) \(777600\) \(1.9615\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 47190.cq have rank \(0\).

Complex multiplication

The elliptic curves in class 47190.cq do not have complex multiplication.

Modular form 47190.2.a.cq

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + 4 q^{7} + q^{8} + q^{9} - q^{10} + q^{12} - q^{13} + 4 q^{14} - q^{15} + q^{16} + q^{18} + q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.