Properties

Label 43120by
Number of curves $2$
Conductor $43120$
CM no
Rank $2$
Graph

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Show commands: SageMath
E = EllipticCurve("by1")
 
E.isogeny_class()
 

Elliptic curves in class 43120by

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
43120.f2 43120by1 \([0, 1, 0, -8976, 331540]\) \(-56933326423/1464100\) \(-2056955084800\) \([2]\) \(86016\) \(1.1461\) \(\Gamma_0(N)\)-optimal
43120.f1 43120by2 \([0, 1, 0, -144496, 21093204]\) \(237487154804983/151250\) \(212495360000\) \([2]\) \(172032\) \(1.4927\)  

Rank

sage: E.rank()
 

The elliptic curves in class 43120by have rank \(2\).

Complex multiplication

The elliptic curves in class 43120by do not have complex multiplication.

Modular form 43120.2.a.by

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} - q^{5} + q^{9} + q^{11} - 6 q^{13} + 2 q^{15} - 4 q^{17} + 2 q^{19} + O(q^{20})\) 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 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.