# Properties

 Label 5520.w Number of curves $2$ Conductor $5520$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("w1")

sage: E.isogeny_class()

## Elliptic curves in class 5520.w

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5520.w1 5520bb1 $$[0, 1, 0, -21, 30]$$ $$67108864/1725$$ $$27600$$ $$[2]$$ $$480$$ $$-0.36567$$ $$\Gamma_0(N)$$-optimal
5520.w2 5520bb2 $$[0, 1, 0, 4, 120]$$ $$21296/23805$$ $$-6094080$$ $$[2]$$ $$960$$ $$-0.019099$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form5520.2.a.w

sage: E.q_eigenform(10)

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

## 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.