# Properties

 Label 176400oa Number of curves $6$ Conductor $176400$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("176400.cg1")

sage: E.isogeny_class()

## Elliptic curves in class 176400oa

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
176400.cg4 176400oa1 [0, 0, 0, -1933050, -1034445125] [2] 2359296 $$\Gamma_0(N)$$-optimal
176400.cg3 176400oa2 [0, 0, 0, -1988175, -972319250] [2, 2] 4718592
176400.cg2 176400oa3 [0, 0, 0, -7500675, 6860943250] [2, 2] 9437184
176400.cg5 176400oa4 [0, 0, 0, 2642325, -4829525750] [2] 9437184
176400.cg1 176400oa5 [0, 0, 0, -115545675, 478045188250] [2] 18874368
176400.cg6 176400oa6 [0, 0, 0, 12344325, 37005498250] [2] 18874368

## Rank

sage: E.rank()

The elliptic curves in class 176400oa have rank $$1$$.

## Modular form 176400.2.a.cg

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.