Properties

Label 450528.q
Number of curves $2$
Conductor $450528$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 450528.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
450528.q1 450528q2 \([0, -1, 0, -12033, -174831]\) \(1000000/507\) \(97698863788032\) \([2]\) \(912384\) \(1.3769\)  
450528.q2 450528q1 \([0, -1, 0, -6618, 207468]\) \(10648000/117\) \(352279556928\) \([2]\) \(456192\) \(1.0303\) \(\Gamma_0(N)\)-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 0 curves highlighted, and conditionally curve 450528.q1.

Rank

sage: E.rank()
 

The elliptic curves in class 450528.q have rank \(0\).

Complex multiplication

The elliptic curves in class 450528.q do not have complex multiplication.

Modular form 450528.2.a.q

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.