Properties

Label 2880.bc
Number of curves $8$
Conductor $2880$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bc1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2880.bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2880.bc1 2880bd7 \([0, 0, 0, -1244172, -534156784]\) \(1114544804970241/405\) \(77396705280\) \([2]\) \(16384\) \(1.8799\)  
2880.bc2 2880bd5 \([0, 0, 0, -77772, -8343664]\) \(272223782641/164025\) \(31345665638400\) \([2, 2]\) \(8192\) \(1.5333\)  
2880.bc3 2880bd8 \([0, 0, 0, -63372, -11528944]\) \(-147281603041/215233605\) \(-41131782450708480\) \([2]\) \(16384\) \(1.8799\)  
2880.bc4 2880bd4 \([0, 0, 0, -46092, 3808784]\) \(56667352321/15\) \(2866544640\) \([2]\) \(4096\) \(1.1867\)  
2880.bc5 2880bd3 \([0, 0, 0, -5772, -78064]\) \(111284641/50625\) \(9674588160000\) \([2, 2]\) \(4096\) \(1.1867\)  
2880.bc6 2880bd2 \([0, 0, 0, -2892, 59024]\) \(13997521/225\) \(42998169600\) \([2, 2]\) \(2048\) \(0.84018\)  
2880.bc7 2880bd1 \([0, 0, 0, -12, 2576]\) \(-1/15\) \(-2866544640\) \([2]\) \(1024\) \(0.49360\) \(\Gamma_0(N)\)-optimal
2880.bc8 2880bd6 \([0, 0, 0, 20148, -586096]\) \(4733169839/3515625\) \(-671846400000000\) \([2]\) \(8192\) \(1.5333\)  

Rank

sage: E.rank()
 

The elliptic curves in class 2880.bc have rank \(0\).

Complex multiplication

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

Modular form 2880.2.a.bc

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

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 16 & 4 & 8 & 16 & 8 \\ 2 & 1 & 2 & 8 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 16 & 4 & 8 & 16 & 8 \\ 16 & 8 & 16 & 1 & 4 & 2 & 4 & 8 \\ 4 & 2 & 4 & 4 & 1 & 2 & 4 & 2 \\ 8 & 4 & 8 & 2 & 2 & 1 & 2 & 4 \\ 16 & 8 & 16 & 4 & 4 & 2 & 1 & 8 \\ 8 & 4 & 8 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.