Properties

Label 190575.bj
Number of curves $2$
Conductor $190575$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bj1")
 
E.isogeny_class()
 

Elliptic curves in class 190575.bj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
190575.bj1 190575by2 \([1, -1, 1, -70445, 5267782]\) \(8869743/2401\) \(10465249253295375\) \([2]\) \(1105920\) \(1.7819\)  
190575.bj2 190575by1 \([1, -1, 1, 11230, 530632]\) \(35937/49\) \(-213576515373375\) \([2]\) \(552960\) \(1.4353\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 190575.bj have rank \(1\).

Complex multiplication

The elliptic curves in class 190575.bj do not have complex multiplication.

Modular form 190575.2.a.bj

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