# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("2880.bc1")

sage: E.isogeny_class()

## Elliptic curves in class 2880.bc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2880.bc1 2880bd7 [0, 0, 0, -1244172, -534156784] [2] 16384
2880.bc2 2880bd5 [0, 0, 0, -77772, -8343664] [2, 2] 8192
2880.bc3 2880bd8 [0, 0, 0, -63372, -11528944] [2] 16384
2880.bc4 2880bd4 [0, 0, 0, -46092, 3808784] [2] 4096
2880.bc5 2880bd3 [0, 0, 0, -5772, -78064] [2, 2] 4096
2880.bc6 2880bd2 [0, 0, 0, -2892, 59024] [2, 2] 2048
2880.bc7 2880bd1 [0, 0, 0, -12, 2576] [2] 1024 $$\Gamma_0(N)$$-optimal
2880.bc8 2880bd6 [0, 0, 0, 20148, -586096] [2] 8192

## Rank

sage: E.rank()

The elliptic curves in class 2880.bc have rank $$0$$.

## Modular form2880.2.a.bc

sage: E.q_eigenform(10)

$$q + q^{5} + 4q^{11} + 2q^{13} - 2q^{17} + 4q^{19} + O(q^{20})$$

## 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.