# Properties

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

# Related objects

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 form2880.2.a.bb

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.