Properties

Label 43120.bw
Number of curves $2$
Conductor $43120$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bw1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 43120.bw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
43120.bw1 43120w1 \([0, 0, 0, -1862, -29841]\) \(379275264/15125\) \(28471058000\) \([2]\) \(34560\) \(0.77253\) \(\Gamma_0(N)\)-optimal
43120.bw2 43120w2 \([0, 0, 0, 833, -109074]\) \(2122416/171875\) \(-5176556000000\) \([2]\) \(69120\) \(1.1191\)  

Rank

sage: E.rank()
 

The elliptic curves in class 43120.bw have rank \(0\).

Complex multiplication

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

Modular form 43120.2.a.bw

sage: E.q_eigenform(10)
 
\(q + q^{5} - 3q^{9} + q^{11} - 8q^{19} + O(q^{20})\)  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.