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Properties

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

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Show commands: SageMath
E = EllipticCurve("ba1")
 
E.isogeny_class()
 

Elliptic curves in class 151725ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
151725.y1 151725ba1 \([1, 1, 1, -5208, 137856]\) \(5177717/189\) \(570250067625\) \([2]\) \(236544\) \(1.0254\) \(\Gamma_0(N)\)-optimal
151725.y2 151725ba2 \([1, 1, 1, 2017, 499106]\) \(300763/35721\) \(-107777262781125\) \([2]\) \(473088\) \(1.3720\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 151725.2.a.ba

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} - q^{4} + q^{6} + q^{7} + 3 q^{8} + q^{9} + 6 q^{11} + q^{12} - 2 q^{13} - q^{14} - q^{16} - q^{18} - 6 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.