# Properties

 Label 8880ba Number of curves $6$ Conductor $8880$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("8880.ba1")

sage: E.isogeny_class()

## Elliptic curves in class 8880ba

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
8880.ba5 8880ba1 [0, 1, 0, -13520, -2087532] [2] 41472 $$\Gamma_0(N)$$-optimal
8880.ba4 8880ba2 [0, 1, 0, -341200, -76667500] [2, 2] 82944
8880.ba1 8880ba3 [0, 1, 0, -5456080, -4907160172] [2] 165888
8880.ba3 8880ba4 [0, 1, 0, -469200, -14049900] [2, 4] 165888
8880.ba2 8880ba5 [0, 1, 0, -4850000, 4091635860] [4] 331776
8880.ba6 8880ba6 [0, 1, 0, 1863600, -110161260] [4] 331776

## Rank

sage: E.rank()

The elliptic curves in class 8880ba have rank $$1$$.

## Modular form8880.2.a.ba

sage: E.q_eigenform(10)

$$q + q^{3} + q^{5} + q^{9} - 4q^{11} - 2q^{13} + q^{15} + 2q^{17} - 4q^{19} + O(q^{20})$$

## 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 Cremona numbering.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.