Properties

Label 61446.cv
Number of curves $2$
Conductor $61446$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("cv1")
 
E.isogeny_class()
 

Elliptic curves in class 61446.cv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
61446.cv1 61446de2 \([1, 0, 0, -16743266, -11929605948]\) \(10593712059133697959507441/4876213982377385856384\) \(238934485136491906962816\) \([7]\) \(6750240\) \(3.1806\)  
61446.cv2 61446de1 \([1, 0, 0, -14044626, -20259954786]\) \(6252564350146719590876401/1254\) \(61446\) \([]\) \(964320\) \(2.2077\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 61446.cv have rank \(0\).

Complex multiplication

The elliptic curves in class 61446.cv do not have complex multiplication.

Modular form 61446.2.a.cv

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

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.