# Properties

 Label 176400kd Number of curves $4$ Conductor $176400$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("176400.lf1")

sage: E.isogeny_class()

## Elliptic curves in class 176400kd

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
176400.lf2 176400kd1 [0, 0, 0, -2061675, 1137988250] [2] 2654208 $$\Gamma_0(N)$$-optimal
176400.lf3 176400kd2 [0, 0, 0, -1473675, 1800664250] [2] 5308416
176400.lf1 176400kd3 [0, 0, 0, -8235675, -7971405750] [2] 7962624
176400.lf4 176400kd4 [0, 0, 0, 12932325, -42200061750] [2] 15925248

## Rank

sage: E.rank()

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

## Modular form 176400.2.a.lf

sage: E.q_eigenform(10)

$$q + 2q^{13} + 2q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.