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Properties

Label 59150a
Number of curves $2$
Conductor $59150$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 59150a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
59150.i2 59150a1 \([1, 1, 0, 1742725, 3533468125]\) \(45924354671/449576960\) \(-5730214651965440000000\) \([]\) \(3234816\) \(2.8562\) \(\Gamma_0(N)\)-optimal
59150.i1 59150a2 \([1, 1, 0, -15833275, -100569179875]\) \(-34440478374289/322828856000\) \(-4114709616632580875000000\) \([]\) \(9704448\) \(3.4055\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 59150.2.a.a

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.