# Properties

 Label 154560.dx Number of curves $2$ Conductor $154560$ CM no Rank $1$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 154560.dx

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
154560.dx1 154560gm1 $$[0, -1, 0, -1505, 12897]$$ $$1439069689/579600$$ $$151938662400$$ $$[2]$$ $$147456$$ $$0.84352$$ $$\Gamma_0(N)$$-optimal
154560.dx2 154560gm2 $$[0, -1, 0, 4895, 88417]$$ $$49471280711/41992020$$ $$-11007956090880$$ $$[2]$$ $$294912$$ $$1.1901$$

## Rank

sage: E.rank()

The elliptic curves in class 154560.dx have rank $$1$$.

## Complex multiplication

The elliptic curves in class 154560.dx do not have complex multiplication.

## Modular form 154560.2.a.dx

sage: E.q_eigenform(10)

$$q - q^{3} + q^{5} + q^{7} + q^{9} + 2q^{11} - 4q^{13} - q^{15} - 6q^{17} + 4q^{19} + O(q^{20})$$

## 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 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.