Properties

Label 84150.gi
Number of curves $2$
Conductor $84150$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("gi1")
 
E.isogeny_class()
 

Elliptic curves in class 84150.gi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
84150.gi1 84150ga2 \([1, -1, 1, -40955, -3179703]\) \(666940371553/37026\) \(421749281250\) \([2]\) \(196608\) \(1.2960\)  
84150.gi2 84150ga1 \([1, -1, 1, -2705, -43203]\) \(192100033/38148\) \(434529562500\) \([2]\) \(98304\) \(0.94944\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 84150.gi have rank \(1\).

Complex multiplication

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

Modular form 84150.2.a.gi

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