Properties

Label 2880bb
Number of curves $8$
Conductor $2880$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2880bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2880.q8 2880bb1 \([0, 0, 0, 852, 29392]\) \(357911/2160\) \(-412782428160\) \([2]\) \(3072\) \(0.91074\) \(\Gamma_0(N)\)-optimal
2880.q6 2880bb2 \([0, 0, 0, -10668, 384208]\) \(702595369/72900\) \(13931406950400\) \([2, 2]\) \(6144\) \(1.2573\)  
2880.q7 2880bb3 \([0, 0, 0, -7788, -865712]\) \(-273359449/1536000\) \(-293534171136000\) \([2]\) \(9216\) \(1.4600\)  
2880.q5 2880bb4 \([0, 0, 0, -39468, -2599472]\) \(35578826569/5314410\) \(1015599566684160\) \([2]\) \(12288\) \(1.6039\)  
2880.q4 2880bb5 \([0, 0, 0, -166188, 26076112]\) \(2656166199049/33750\) \(6449725440000\) \([2]\) \(12288\) \(1.6039\)  
2880.q3 2880bb6 \([0, 0, 0, -192108, -32347568]\) \(4102915888729/9000000\) \(1719926784000000\) \([2, 2]\) \(18432\) \(1.8066\)  
2880.q1 2880bb7 \([0, 0, 0, -3072108, -2072539568]\) \(16778985534208729/81000\) \(15479341056000\) \([2]\) \(36864\) \(2.1532\)  
2880.q2 2880bb8 \([0, 0, 0, -261228, -6994352]\) \(10316097499609/5859375000\) \(1119744000000000000\) \([2]\) \(36864\) \(2.1532\)  

Rank

sage: E.rank()
 

The elliptic curves in class 2880bb have rank \(1\).

Complex multiplication

The elliptic curves in class 2880bb do not have complex multiplication.

Modular form 2880.2.a.bb

sage: E.q_eigenform(10)
 
\(q - q^{5} + 4q^{7} - 2q^{13} - 6q^{17} - 4q^{19} + O(q^{20})\)  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 Cremona numbering.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.