Properties

Label 37026.z
Number of curves $2$
Conductor $37026$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("z1")
 
E.isogeny_class()
 

Elliptic curves in class 37026.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
37026.z1 37026bl2 \([1, -1, 1, -198221, 34016051]\) \(666940371553/37026\) \(47817893020194\) \([2]\) \(184320\) \(1.6902\)  
37026.z2 37026bl1 \([1, -1, 1, -13091, 470495]\) \(192100033/38148\) \(49266920081412\) \([2]\) \(92160\) \(1.3437\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 37026.z have rank \(1\).

Complex multiplication

The elliptic curves in class 37026.z do not have complex multiplication.

Modular form 37026.2.a.z

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - 2 q^{5} + 2 q^{7} + q^{8} - 2 q^{10} - 4 q^{13} + 2 q^{14} + q^{16} + q^{17} - 2 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.