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Properties

Label 162450.eu
Number of curves $2$
Conductor $162450$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("eu1")
 
E.isogeny_class()
 

Elliptic curves in class 162450.eu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
162450.eu1 162450ck2 \([1, -1, 1, -4888730, -4119188103]\) \(651038076963/7220000\) \(143298813158437500000\) \([2]\) \(11059200\) \(2.6819\)  
162450.eu2 162450ck1 \([1, -1, 1, -556730, 56859897]\) \(961504803/486400\) \(9653814781200000000\) \([2]\) \(5529600\) \(2.3354\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 162450.eu have rank \(1\).

Complex multiplication

The elliptic curves in class 162450.eu do not have complex multiplication.

Modular form 162450.2.a.eu

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + 4 q^{7} + q^{8} - 6 q^{11} + 4 q^{14} + q^{16} - 4 q^{17} + O(q^{20})\) 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.