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Properties

Label 163254cr
Number of curves $2$
Conductor $163254$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("cr1")
 
E.isogeny_class()
 

Elliptic curves in class 163254cr

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
163254.bv2 163254cr1 \([1, 0, 1, 503, 19268]\) \(2924207/34776\) \(-167857109784\) \([]\) \(246240\) \(0.83477\) \(\Gamma_0(N)\)-optimal
163254.bv1 163254cr2 \([1, 0, 1, -4567, -542488]\) \(-2181825073/25039686\) \(-120861781741974\) \([]\) \(738720\) \(1.3841\)  

Rank

sage: E.rank()
 

The elliptic curves in class 163254cr have rank \(0\).

Complex multiplication

The elliptic curves in class 163254cr do not have complex multiplication.

Modular form 163254.2.a.cr

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} + 3 q^{5} - q^{6} - q^{7} - q^{8} + q^{9} - 3 q^{10} + q^{12} + q^{14} + 3 q^{15} + q^{16} - q^{18} - 8 q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.