# Properties

 Label 5520.x Number of curves $4$ Conductor $5520$ CM no Rank $0$ Graph # Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("x1")

sage: E.isogeny_class()

## Elliptic curves in class 5520.x

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5520.x1 5520ba4 $$[0, 1, 0, -22118576, 40031686740]$$ $$292169767125103365085489/72534787200$$ $$297102488371200$$ $$$$ $$172032$$ $$2.5928$$
5520.x2 5520ba3 $$[0, 1, 0, -1618096, 397291604]$$ $$114387056741228939569/49503729150000000$$ $$202767274598400000000$$ $$$$ $$172032$$ $$2.5928$$
5520.x3 5520ba2 $$[0, 1, 0, -1382576, 624992340]$$ $$71356102305927901489/35540674560000$$ $$145574602997760000$$ $$[2, 2]$$ $$86016$$ $$2.2462$$
5520.x4 5520ba1 $$[0, 1, 0, -71856, 13148244]$$ $$-10017490085065009/12502381363200$$ $$-51209754063667200$$ $$$$ $$43008$$ $$1.8996$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 5520.x have rank $$0$$.

## Complex multiplication

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

## Modular form5520.2.a.x

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} + q^{9} + 6q^{13} - q^{15} + 2q^{17} + O(q^{20})$$ ## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 