# Properties

 Label 176400dx Number of curves $4$ Conductor $176400$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("dx1")

sage: E.isogeny_class()

## Elliptic curves in class 176400dx

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
176400.cj3 176400dx1 [0, 0, 0, -621075, 118935250]  3538944 $$\Gamma_0(N)$$-optimal
176400.cj2 176400dx2 [0, 0, 0, -4149075, -3165632750] [2, 2] 7077888
176400.cj4 176400dx3 [0, 0, 0, 1142925, -10685564750]  14155776
176400.cj1 176400dx4 [0, 0, 0, -65889075, -205858052750]  14155776

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 176400.2.a.dx

sage: E.q_eigenform(10)

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

## 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 Cremona numbering.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 