# Properties

 Label 388080.nq Number of curves $6$ Conductor $388080$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("388080.nq1")

sage: E.isogeny_class()

## Elliptic curves in class 388080.nq

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
388080.nq1 388080nq5 [0, 0, 0, -93492147, 347928497714] [2] 50331648
388080.nq2 388080nq3 [0, 0, 0, -6174147, 4786221314] [2, 2] 25165824
388080.nq3 388080nq2 [0, 0, 0, -1905267, -945176974] [2, 2] 12582912
388080.nq4 388080nq1 [0, 0, 0, -1869987, -984246046] [2] 6291456 $$\Gamma_0(N)$$-optimal
388080.nq5 388080nq4 [0, 0, 0, 1799133, -4176154654] [2] 25165824
388080.nq6 388080nq6 [0, 0, 0, 12841773, 28453435346] [2] 50331648

## Rank

sage: E.rank()

The elliptic curves in class 388080.nq have rank $$0$$.

## Modular form 388080.2.a.nq

sage: E.q_eigenform(10)

$$q + q^{5} + q^{11} + 2q^{13} - 6q^{17} - 4q^{19} + O(q^{20})$$

## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.