Properties

Label 162288fh
Number of curves $2$
Conductor $162288$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("fh1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 162288fh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
162288.dp2 162288fh1 \([0, 0, 0, -12495, -690802]\) \(-9826000/3703\) \(-81303538192128\) \([2]\) \(368640\) \(1.3789\) \(\Gamma_0(N)\)-optimal
162288.dp1 162288fh2 \([0, 0, 0, -215355, -38463334]\) \(12576878500/1127\) \(98978220407808\) \([2]\) \(737280\) \(1.7255\)  

Rank

sage: E.rank()
 

The elliptic curves in class 162288fh have rank \(0\).

Complex multiplication

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

Modular form 162288.2.a.fh

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.