Properties

Label 450.g
Number of curves $4$
Conductor $450$
CM no
Rank $0$
Graph

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

Elliptic curves in class 450.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
450.g1 450b2 \([1, -1, 1, -1130, 14897]\) \(-349938025/8\) \(-3645000\) \([3]\) \(180\) \(0.37251\)  
450.g2 450b3 \([1, -1, 1, -680, -8053]\) \(-121945/32\) \(-9112500000\) \([]\) \(300\) \(0.62793\)  
450.g3 450b1 \([1, -1, 1, -5, 47]\) \(-25/2\) \(-911250\) \([]\) \(60\) \(-0.17679\) \(\Gamma_0(N)\)-optimal
450.g4 450b4 \([1, -1, 1, 4945, 59447]\) \(46969655/32768\) \(-9331200000000\) \([3]\) \(900\) \(1.1772\)  

Rank

sage: E.rank()
 

The elliptic curves in class 450.g have rank \(0\).

Complex multiplication

The elliptic curves in class 450.g do not have complex multiplication.

Modular form 450.2.a.g

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + 2 q^{7} + q^{8} + 3 q^{11} - 4 q^{13} + 2 q^{14} + q^{16} + 3 q^{17} + 5 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 15 & 3 & 5 \\ 15 & 1 & 5 & 3 \\ 3 & 5 & 1 & 15 \\ 5 & 3 & 15 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.