# Properties

 Label 273600.pq Number of curves $4$ Conductor $273600$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("273600.pq1")

sage: E.isogeny_class()

## Elliptic curves in class 273600.pq

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
273600.pq1 273600pq3 [0, 0, 0, -43776300, 111482498000] [2] 14155776
273600.pq2 273600pq4 [0, 0, 0, -3168300, 1154882000] [2] 14155776
273600.pq3 273600pq2 [0, 0, 0, -2736300, 1741538000] [2, 2] 7077888
273600.pq4 273600pq1 [0, 0, 0, -144300, 36002000] [2] 3538944 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 273600.pq have rank $$1$$.

## Modular form 273600.2.a.pq

sage: E.q_eigenform(10)

$$q + 4q^{7} + 4q^{11} - 2q^{13} - 2q^{17} - q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.