Properties

Label 84150.hc
Number of curves $2$
Conductor $84150$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("hc1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 84150.hc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
84150.hc1 84150fr1 \([1, -1, 1, -203405, -34979403]\) \(81706955619457/744505344\) \(8480381184000000\) \([2]\) \(1146880\) \(1.8786\) \(\Gamma_0(N)\)-optimal
84150.hc2 84150fr2 \([1, -1, 1, -59405, -83651403]\) \(-2035346265217/264305213568\) \(-3010601573298000000\) \([2]\) \(2293760\) \(2.2252\)  

Rank

sage: E.rank()
 

The elliptic curves in class 84150.hc have rank \(0\).

Complex multiplication

The elliptic curves in class 84150.hc do not have complex multiplication.

Modular form 84150.2.a.hc

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