Properties

Label 342225bt
Number of curves $2$
Conductor $342225$
CM no
Rank $1$
Graph

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

Elliptic curves in class 342225bt

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
342225.bt2 342225bt1 \([0, 0, 1, -76050, 8032781]\) \(884736/5\) \(274901856328125\) \([]\) \(1244160\) \(1.6126\) \(\Gamma_0(N)\)-optimal
342225.bt1 342225bt2 \([0, 0, 1, -456300, -113076844]\) \(2359296/125\) \(556676259064453125\) \([]\) \(3732480\) \(2.1619\)  

Rank

sage: E.rank()
 

The elliptic curves in class 342225bt have rank \(1\).

Complex multiplication

The elliptic curves in class 342225bt do not have complex multiplication.

Modular form 342225.2.a.bt

sage: E.q_eigenform(10)
 
\(q - 2 q^{4} + 2 q^{7} + 3 q^{11} + 4 q^{16} + 6 q^{17} + q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.