# Properties

 Label 5520.f Number of curves $4$ Conductor $5520$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("f1")

sage: E.isogeny_class()

## Elliptic curves in class 5520.f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5520.f1 5520m3 $$[0, -1, 0, -170296, -26932880]$$ $$133345896593725369/340006815000$$ $$1392667914240000$$ $$[2]$$ $$46080$$ $$1.7823$$
5520.f2 5520m2 $$[0, -1, 0, -14776, -59024]$$ $$87109155423289/49979073600$$ $$204714285465600$$ $$[2, 2]$$ $$23040$$ $$1.4357$$
5520.f3 5520m1 $$[0, -1, 0, -9656, 366960]$$ $$24310870577209/114462720$$ $$468839301120$$ $$[2]$$ $$11520$$ $$1.0891$$ $$\Gamma_0(N)$$-optimal
5520.f4 5520m4 $$[0, -1, 0, 58824, -530064]$$ $$5495662324535111/3207841648920$$ $$-13139319393976320$$ $$[2]$$ $$46080$$ $$1.7823$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form5520.2.a.f

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.