# Properties

 Label 5780.f Number of curves $4$ Conductor $5780$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 5780.f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5780.f1 5780e3 $$[0, -1, 0, -11945, -498418]$$ $$488095744/125$$ $$48275138000$$ $$$$ $$6912$$ $$1.0360$$
5780.f2 5780e4 $$[0, -1, 0, -10500, -625000]$$ $$-20720464/15625$$ $$-96550276000000$$ $$$$ $$13824$$ $$1.3825$$
5780.f3 5780e1 $$[0, -1, 0, -385, 2130]$$ $$16384/5$$ $$1931005520$$ $$$$ $$2304$$ $$0.48666$$ $$\Gamma_0(N)$$-optimal
5780.f4 5780e2 $$[0, -1, 0, 1060, 13112]$$ $$21296/25$$ $$-154480441600$$ $$$$ $$4608$$ $$0.83323$$

## Rank

sage: E.rank()

The elliptic curves in class 5780.f have rank $$1$$.

## Complex multiplication

The elliptic curves in class 5780.f do not have complex multiplication.

## Modular form5780.2.a.f

sage: E.q_eigenform(10)

$$q + 2q^{3} + q^{5} - 2q^{7} + q^{9} + 2q^{13} + 2q^{15} - 4q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 