Properties

Label 53235g
Number of curves $3$
Conductor $53235$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 53235g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
53235.q2 53235g1 \([0, 0, 1, -2028, -38997]\) \(-262144/35\) \(-123156031635\) \([]\) \(41040\) \(0.86063\) \(\Gamma_0(N)\)-optimal
53235.q3 53235g2 \([0, 0, 1, 13182, 99414]\) \(71991296/42875\) \(-150866138752875\) \([]\) \(123120\) \(1.4099\)  
53235.q1 53235g3 \([0, 0, 1, -199758, 35947863]\) \(-250523582464/13671875\) \(-48107824857421875\) \([]\) \(369360\) \(1.9592\)  

Rank

sage: E.rank()
 

The elliptic curves in class 53235g have rank \(0\).

Complex multiplication

The elliptic curves in class 53235g do not have complex multiplication.

Modular form 53235.2.a.g

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

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.