# Properties

 Label 176400qp Number of curves $2$ Conductor $176400$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("qp1")

sage: E.isogeny_class()

## Elliptic curves in class 176400qp

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
176400.sj2 176400qp1 $$[0, 0, 0, 437325, -121850750]$$ $$19652/25$$ $$-11767111801200000000$$ $$$$ $$3096576$$ $$2.3453$$ $$\Gamma_0(N)$$-optimal
176400.sj1 176400qp2 $$[0, 0, 0, -2649675, -1180691750]$$ $$2185454/625$$ $$588355590060000000000$$ $$$$ $$6193152$$ $$2.6919$$

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 176400qp do not have complex multiplication.

## Modular form 176400.2.a.qp

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 