Properties

Label 81120.bw
Number of curves $4$
Conductor $81120$
CM no
Rank $1$
Graph

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

Elliptic curves in class 81120.bw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
81120.bw1 81120u4 \([0, 1, 0, -175985, -28474497]\) \(30488290624/195\) \(3855268884480\) \([2]\) \(258048\) \(1.5997\)  
81120.bw2 81120u3 \([0, 1, 0, -36560, 2176188]\) \(2186875592/428415\) \(1058753217400320\) \([2]\) \(258048\) \(1.5997\)  
81120.bw3 81120u1 \([0, 1, 0, -11210, -429792]\) \(504358336/38025\) \(11746522382400\) \([2, 2]\) \(129024\) \(1.2531\) \(\Gamma_0(N)\)-optimal
81120.bw4 81120u2 \([0, 1, 0, 10760, -1888600]\) \(55742968/658125\) \(-1626441560640000\) \([4]\) \(258048\) \(1.5997\)  

Rank

sage: E.rank()
 

The elliptic curves in class 81120.bw have rank \(1\).

Complex multiplication

The elliptic curves in class 81120.bw do not have complex multiplication.

Modular form 81120.2.a.bw

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

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.