# Properties

 Label 4080.ba Number of curves $8$ Conductor $4080$ CM no Rank $1$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 4080.ba

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4080.ba1 4080be7 [0, 1, 0, -1815520, 940954100] [8] 49152
4080.ba2 4080be3 [0, 1, 0, -348160, -79187020] [2] 12288
4080.ba3 4080be5 [0, 1, 0, -115520, 14114100] [2, 4] 24576
4080.ba4 4080be4 [0, 1, 0, -23040, -1089612] [2, 4] 12288
4080.ba5 4080be2 [0, 1, 0, -21760, -1242700] [2, 2] 6144
4080.ba6 4080be1 [0, 1, 0, -1280, -22092] [2] 3072 $$\Gamma_0(N)$$-optimal
4080.ba7 4080be6 [0, 1, 0, 48960, -6475212] [4] 24576
4080.ba8 4080be8 [0, 1, 0, 104800, 61791348] [4] 49152

## Rank

sage: E.rank()

The elliptic curves in class 4080.ba have rank $$1$$.

## Complex multiplication

The elliptic curves in class 4080.ba do not have complex multiplication.

## Modular form4080.2.a.ba

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.