# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("2880.q1")

sage: E.isogeny_class()

## Elliptic curves in class 2880bb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2880.q8 2880bb1 [0, 0, 0, 852, 29392] [2] 3072 $$\Gamma_0(N)$$-optimal
2880.q6 2880bb2 [0, 0, 0, -10668, 384208] [2, 2] 6144
2880.q7 2880bb3 [0, 0, 0, -7788, -865712] [2] 9216
2880.q5 2880bb4 [0, 0, 0, -39468, -2599472] [2] 12288
2880.q4 2880bb5 [0, 0, 0, -166188, 26076112] [2] 12288
2880.q3 2880bb6 [0, 0, 0, -192108, -32347568] [2, 2] 18432
2880.q1 2880bb7 [0, 0, 0, -3072108, -2072539568] [2] 36864
2880.q2 2880bb8 [0, 0, 0, -261228, -6994352] [2] 36864

## Rank

sage: E.rank()

The elliptic curves in class 2880bb have rank $$1$$.

## Modular form2880.2.a.q

sage: E.q_eigenform(10)

$$q - q^{5} + 4q^{7} - 2q^{13} - 6q^{17} - 4q^{19} + O(q^{20})$$

## 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 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.