Properties

Label 433200gt
Number of curves $2$
Conductor $433200$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("433200.gt1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 433200gt

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
433200.gt2 433200gt1 [0, 1, 0, -584408, -237976812] [2] 5898240 \(\Gamma_0(N)\)-optimal*
433200.gt1 433200gt2 [0, 1, 0, -10312408, -12748184812] [2] 11796480 \(\Gamma_0(N)\)-optimal*
*optimality has not been proved rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 433200gt1.

Rank

sage: E.rank()
 

The elliptic curves in class 433200gt have rank \(1\).

Modular form 433200.2.a.gt

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.