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Properties

Label 151725.d
Number of curves $2$
Conductor $151725$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 151725.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
151725.d1 151725i2 \([0, -1, 1, -718730958, 7416716358068]\) \(886385087098880/21\) \(972791174389453125\) \([]\) \(50592000\) \(3.4241\)  
151725.d2 151725i1 \([0, -1, 1, -1678608, -3713182]\) \(7057510400/4084101\) \(302703040618296373125\) \([]\) \(10118400\) \(2.6194\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 151725.d have rank \(0\).

Complex multiplication

The elliptic curves in class 151725.d do not have complex multiplication.

Modular form 151725.2.a.d

sage: E.q_eigenform(10)
 
\(q - 2 q^{2} - q^{3} + 2 q^{4} + 2 q^{6} - q^{7} + q^{9} + 5 q^{11} - 2 q^{12} - 4 q^{13} + 2 q^{14} - 4 q^{16} - 2 q^{18} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.