Properties

Label 369600tq
Number of curves $2$
Conductor $369600$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("tq1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 369600tq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
369600.tq2 369600tq1 \([0, 1, 0, -14833, 652463]\) \(11279504/693\) \(22176000000000\) \([2]\) \(737280\) \(1.3127\) \(\Gamma_0(N)\)-optimal
369600.tq1 369600tq2 \([0, 1, 0, -44833, -2857537]\) \(77860436/17787\) \(2276736000000000\) \([2]\) \(1474560\) \(1.6593\)  

Rank

sage: E.rank()
 

The elliptic curves in class 369600tq have rank \(0\).

Complex multiplication

The elliptic curves in class 369600tq do not have complex multiplication.

Modular form 369600.2.a.tq

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{7} + q^{9} - q^{11} + 4 q^{13} + 2 q^{17} - 4 q^{19} + O(q^{20})\) 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 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.