# Properties

 Label 5520.k Number of curves $2$ Conductor $5520$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("k1")

sage: E.isogeny_class()

## Elliptic curves in class 5520.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5520.k1 5520d2 $$[0, -1, 0, -518720, -143623200]$$ $$7536914291382802562/17961229575$$ $$36784598169600$$ $$$$ $$42240$$ $$1.8444$$
5520.k2 5520d1 $$[0, -1, 0, -32040, -2291328]$$ $$-3552342505518244/179863605135$$ $$-184180331658240$$ $$$$ $$21120$$ $$1.4978$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 5520.k have rank $$1$$.

## Complex multiplication

The elliptic curves in class 5520.k do not have complex multiplication.

## Modular form5520.2.a.k

sage: E.q_eigenform(10)

$$q - q^{3} + q^{5} + q^{9} - 2 q^{11} - q^{15} + 6 q^{17} - 8 q^{19} + O(q^{20})$$

## 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 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. 