# Properties

 Label 242550.nq Number of curves 4 Conductor 242550 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("242550.nq1")

sage: E.isogeny_class()

## Elliptic curves in class 242550.nq

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
242550.nq1 242550nq3 [1, -1, 1, -363726005, 2670048155247] [2] 56623104
242550.nq2 242550nq2 [1, -1, 1, -23384255, 39206427747] [2, 2] 28311552
242550.nq3 242550nq1 [1, -1, 1, -5523755, -4337471253] [2] 14155776 $$\Gamma_0(N)$$-optimal
242550.nq4 242550nq4 [1, -1, 1, 31189495, 194959910247] [2] 56623104

## Rank

sage: E.rank()

The elliptic curves in class 242550.nq have rank $$1$$.

## Modular form 242550.2.a.nq

sage: E.q_eigenform(10)

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

## 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 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.