# Properties

 Label 5520.v Number of curves $4$ Conductor $5520$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("v1")

sage: E.isogeny_class()

## Elliptic curves in class 5520.v

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5520.v1 5520g3 $$[0, 1, 0, -1056, -13356]$$ $$63649751618/1164375$$ $$2384640000$$ $$$$ $$3072$$ $$0.59423$$
5520.v2 5520g2 $$[0, 1, 0, -136, 260]$$ $$273671716/119025$$ $$121881600$$ $$[2, 2]$$ $$1536$$ $$0.24766$$
5520.v3 5520g1 $$[0, 1, 0, -116, 444]$$ $$680136784/345$$ $$88320$$ $$$$ $$768$$ $$-0.098917$$ $$\Gamma_0(N)$$-optimal
5520.v4 5520g4 $$[0, 1, 0, 464, 2420]$$ $$5382838942/4197615$$ $$-8596715520$$ $$$$ $$3072$$ $$0.59423$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form5520.2.a.v

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} + q^{9} - 4 q^{11} + 2 q^{13} - q^{15} + 2 q^{17} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 