Properties

Label 162288.cg
Number of curves $2$
Conductor $162288$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("cg1")
 
E.isogeny_class()
 

Elliptic curves in class 162288.cg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
162288.cg1 162288w2 \([0, 0, 0, -98931, 10064306]\) \(304821217/51842\) \(18211992555036672\) \([2]\) \(1327104\) \(1.8407\)  
162288.cg2 162288w1 \([0, 0, 0, -28371, -1690990]\) \(7189057/644\) \(226235932360704\) \([2]\) \(663552\) \(1.4941\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 162288.cg have rank \(1\).

Complex multiplication

The elliptic curves in class 162288.cg do not have complex multiplication.

Modular form 162288.2.a.cg

sage: E.q_eigenform(10)
 
\(q - 2 q^{5} + 6 q^{11} + 4 q^{13} - 2 q^{17} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.