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Properties

Label 189525bm
Number of curves $2$
Conductor $189525$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bm1")
 
E.isogeny_class()
 

Elliptic curves in class 189525bm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
189525.bg1 189525bm1 \([1, 1, 0, -6505, -198200]\) \(5177717/189\) \(1111458938625\) \([2]\) \(314496\) \(1.0810\) \(\Gamma_0(N)\)-optimal
189525.bg2 189525bm2 \([1, 1, 0, 2520, -694575]\) \(300763/35721\) \(-210065739400125\) \([2]\) \(628992\) \(1.4276\)  

Rank

sage: E.rank()
 

The elliptic curves in class 189525bm have rank \(1\).

Complex multiplication

The elliptic curves in class 189525bm do not have complex multiplication.

Modular form 189525.2.a.bm

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} - q^{4} - q^{6} - q^{7} - 3 q^{8} + q^{9} - 6 q^{11} + q^{12} + 2 q^{13} - q^{14} - q^{16} + 4 q^{17} + q^{18} + O(q^{20})\) 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 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.