Properties

Label 224400bt
Number of curves $2$
Conductor $224400$
CM no
Rank $2$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bt1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 224400bt

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
224400.fl1 224400bt1 [0, 1, 0, -78408, 8419188] [2] 737280 \(\Gamma_0(N)\)-optimal
224400.fl2 224400bt2 [0, 1, 0, -62408, 11971188] [2] 1474560  

Rank

sage: E.rank()
 

The elliptic curves in class 224400bt have rank \(2\).

Complex multiplication

The elliptic curves in class 224400bt do not have complex multiplication.

Modular form 224400.2.a.bt

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

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.