# Properties

 Label 154560.a Number of curves $2$ Conductor $154560$ CM no Rank $2$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("a1")

sage: E.isogeny_class()

## Elliptic curves in class 154560.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
154560.a1 154560dl1 $$[0, -1, 0, -15681, -716319]$$ $$1626794704081/83462400$$ $$21879167385600$$ $$$$ $$589824$$ $$1.3176$$ $$\Gamma_0(N)$$-optimal
154560.a2 154560dl2 $$[0, -1, 0, 9919, -2851359]$$ $$411664745519/13605414480$$ $$-3566577773445120$$ $$$$ $$1179648$$ $$1.6642$$

## Rank

sage: E.rank()

The elliptic curves in class 154560.a have rank $$2$$.

## Complex multiplication

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

## Modular form 154560.2.a.a

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} - q^{7} + q^{9} - 6q^{11} + q^{15} + 6q^{17} - 8q^{19} + O(q^{20})$$ ## 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. 