# Properties

 Label 273600.hj Number of curves $4$ Conductor $273600$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("273600.hj1")

sage: E.isogeny_class()

## Elliptic curves in class 273600.hj

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
273600.hj1 273600hj4 [0, 0, 0, -8942700, -10278254000]  9437184
273600.hj2 273600hj2 [0, 0, 0, -734700, -51086000] [2, 2] 4718592
273600.hj3 273600hj1 [0, 0, 0, -446700, 114226000]  2359296 $$\Gamma_0(N)$$-optimal
273600.hj4 273600hj3 [0, 0, 0, 2865300, -403886000]  9437184

## Rank

sage: E.rank()

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

## Modular form 273600.2.a.hj

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 