Properties

Label 1936g
Number of curves 3
Conductor 1936
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("1936.i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1936g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1936.i3 1936g1 [0, 1, 0, -645, 14771] [] 960 \(\Gamma_0(N)\)-optimal
1936.i2 1936g2 [0, 1, 0, -20005, -1979309] [] 4800  
1936.i1 1936g3 [0, 1, 0, -15140165, -22679876749] [] 24000  

Rank

sage: E.rank()
 

The elliptic curves in class 1936g have rank \(1\).

Modular form 1936.2.a.i

sage: E.q_eigenform(10)
 
\( q + q^{3} + q^{5} - 2q^{7} - 2q^{9} - 4q^{13} + q^{15} + 2q^{17} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.