Properties

Label 433200bm
Number of curves $2$
Conductor $433200$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("433200.bm1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 433200bm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
433200.bm2 433200bm1 [0, -1, 0, -210971408, 1631017125312] [2] 112066560 \(\Gamma_0(N)\)-optimal*
433200.bm1 433200bm2 [0, -1, 0, -3722779408, 87417462949312] [2] 224133120 \(\Gamma_0(N)\)-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 433200bm1.

Rank

sage: E.rank()
 

The elliptic curves in class 433200bm have rank \(0\).

Modular form 433200.2.a.bm

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.