# Properties

 Label 238050fn Number of curves $6$ Conductor $238050$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("238050.fn1")

sage: E.isogeny_class()

## Elliptic curves in class 238050fn

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
238050.fn5 238050fn1 [1, -1, 1, -49992980, 149278822647] [2] 38928384 $$\Gamma_0(N)$$-optimal
238050.fn4 238050fn2 [1, -1, 1, -821274980, 9059128486647] [2, 2] 77856768
238050.fn1 238050fn3 [1, -1, 1, -13140362480, 579777814186647] [2] 155713536
238050.fn3 238050fn4 [1, -1, 1, -842699480, 8561565898647] [2, 2] 155713536
238050.fn6 238050fn5 [1, -1, 1, 1046227270, 41481781297647] [2] 311427072
238050.fn2 238050fn6 [1, -1, 1, -3074418230, -56202912226353] [2] 311427072

## Rank

sage: E.rank()

The elliptic curves in class 238050fn have rank $$0$$.

## Modular form 238050.2.a.fn

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + q^{8} + 4q^{11} + 2q^{13} + q^{16} + 6q^{17} - 4q^{19} + O(q^{20})$$

## 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 Cremona 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 Cremona labels.