# Properties

 Label 130050.fm Number of curves 6 Conductor 130050 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("130050.fm1")

sage: E.isogeny_class()

## Elliptic curves in class 130050.fm

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
130050.fm1 130050br5 [1, -1, 1, -1804054955, 29493709544297] [2] 37748736
130050.fm2 130050br3 [1, -1, 1, -112754705, 460849452797] [2, 2] 18874368
130050.fm3 130050br6 [1, -1, 1, -106902455, 510815963297] [2] 37748736
130050.fm4 130050br2 [1, -1, 1, -7414205, 6410535797] [2, 2] 9437184
130050.fm5 130050br1 [1, -1, 1, -2212205, -1173980203] [2] 4718592 $$\Gamma_0(N)$$-optimal
130050.fm6 130050br4 [1, -1, 1, 14694295, 37318218797] [2] 18874368

## Rank

sage: E.rank()

The elliptic curves in class 130050.fm have rank $$1$$.

## Modular form 130050.2.a.fm

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + q^{8} - 4q^{11} + 2q^{13} + q^{16} + 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.