# Properties

 Label 176400.pc Number of curves $2$ Conductor $176400$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("176400.pc1")

sage: E.isogeny_class()

## Elliptic curves in class 176400.pc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
176400.pc1 176400gc1 [0, 0, 0, -2649675, 634464250] [2] 6193152 $$\Gamma_0(N)$$-optimal
176400.pc2 176400gc2 [0, 0, 0, 9698325, 4869828250] [2] 12386304

## Rank

sage: E.rank()

The elliptic curves in class 176400.pc have rank $$0$$.

## Modular form 176400.2.a.pc

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.