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Properties

Label 436425.bx
Number of curves $6$
Conductor $436425$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bx1")
 
E.isogeny_class()
 

Elliptic curves in class 436425.bx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
436425.bx1 436425bx5 \([1, 1, 0, -1231300675, 16629565111000]\) \(89254274298475942657/17457\) \(40379101785515625\) \([2]\) \(69206016\) \(3.4876\) \(\Gamma_0(N)\)-optimal*
436425.bx2 436425bx3 \([1, 1, 0, -76956550, 259811074375]\) \(21790813729717297/304746849\) \(704897979869746265625\) \([2, 2]\) \(34603008\) \(3.1410\) \(\Gamma_0(N)\)-optimal*
436425.bx3 436425bx6 \([1, 1, 0, -74774425, 275240880250]\) \(-19989223566735457/2584262514273\) \(-5977556229840292870265625\) \([2]\) \(69206016\) \(3.4876\)  
436425.bx4 436425bx4 \([1, 1, 0, -18634300, -26859447875]\) \(309368403125137/44372288367\) \(102635799302706300984375\) \([2]\) \(34603008\) \(3.1410\)  
436425.bx5 436425bx2 \([1, 1, 0, -4946425, 3815080000]\) \(5786435182177/627352209\) \(1451103780866075015625\) \([2, 2]\) \(17301504\) \(2.7944\) \(\Gamma_0(N)\)-optimal*
436425.bx6 436425bx1 \([1, 1, 0, 409700, 296105875]\) \(3288008303/18259263\) \(-42234784854528234375\) \([2]\) \(8650752\) \(2.4479\) \(\Gamma_0(N)\)-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 4 curves highlighted, and conditionally curve 436425.bx1.

Rank

sage: E.rank()
 

The elliptic curves in class 436425.bx have rank \(0\).

Complex multiplication

The elliptic curves in class 436425.bx do not have complex multiplication.

Modular form 436425.2.a.bx

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} - q^{4} - q^{6} - 3 q^{8} + q^{9} - q^{11} + q^{12} + 2 q^{13} - q^{16} + 2 q^{17} + q^{18} + 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 8 & 4 & 8 \\ 8 & 4 & 8 & 1 & 2 & 4 \\ 4 & 2 & 4 & 2 & 1 & 2 \\ 8 & 4 & 8 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.