# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("273600.r1")

sage: E.isogeny_class()

## Elliptic curves in class 273600r

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
273600.r4 273600r1 [0, 0, 0, -144300, -36002000] [2] 3538944 $$\Gamma_0(N)$$-optimal
273600.r3 273600r2 [0, 0, 0, -2736300, -1741538000] [2, 2] 7077888
273600.r2 273600r3 [0, 0, 0, -3168300, -1154882000] [2] 14155776
273600.r1 273600r4 [0, 0, 0, -43776300, -111482498000] [2] 14155776

## Rank

sage: E.rank()

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

## Modular form 273600.2.a.r

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 Cremona 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 Cremona labels.