Properties

Label 151725.p
Number of curves $2$
Conductor $151725$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 151725.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
151725.p1 151725bf2 \([1, 1, 1, -29460088, -61558104844]\) \(1526038582697/2205\) \(4085722932435703125\) \([2]\) \(6684672\) \(2.8418\)  
151725.p2 151725bf1 \([1, 1, 1, -1824463, -980814844]\) \(-362467097/14175\) \(-26265361708515234375\) \([2]\) \(3342336\) \(2.4953\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 151725.p have rank \(1\).

Complex multiplication

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

Modular form 151725.2.a.p

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} - q^{4} + q^{6} - q^{7} + 3 q^{8} + q^{9} - 2 q^{11} + q^{12} + 4 q^{13} + q^{14} - q^{16} - q^{18} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.