# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("5780.f1")

sage: E.isogeny_class()

## Elliptic curves in class 5780.f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
5780.f1 5780e3 [0, -1, 0, -11945, -498418]  6912
5780.f2 5780e4 [0, -1, 0, -10500, -625000]  13824
5780.f3 5780e1 [0, -1, 0, -385, 2130]  2304 $$\Gamma_0(N)$$-optimal
5780.f4 5780e2 [0, -1, 0, 1060, 13112]  4608

## Rank

sage: E.rank()

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

## 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. 