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Properties

Label 59150.bv
Number of curves $2$
Conductor $59150$
CM no
Rank $1$
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Show commands: SageMath
E = EllipticCurve("bv1")
 
E.isogeny_class()
 

Elliptic curves in class 59150.bv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
59150.bv1 59150br1 \([1, 0, 0, -413, -3433]\) \(-226981/14\) \(-480593750\) \([]\) \(30720\) \(0.42030\) \(\Gamma_0(N)\)-optimal
59150.bv2 59150br2 \([1, 0, 0, 1212, 206192]\) \(5735339/537824\) \(-18462489500000\) \([]\) \(153600\) \(1.2250\)  

Rank

sage: E.rank()
 

The elliptic curves in class 59150.bv have rank \(1\).

Complex multiplication

The elliptic curves in class 59150.bv do not have complex multiplication.

Modular form 59150.2.a.bv

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} - q^{7} + q^{8} - 2 q^{9} + 5 q^{11} + q^{12} - q^{14} + q^{16} - 2 q^{17} - 2 q^{18} - 4 q^{19} + O(q^{20})\) 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 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.