# Properties

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

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 273600.hj

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
273600.hj1 273600hj4 $$[0, 0, 0, -8942700, -10278254000]$$ $$26487576322129/44531250$$ $$132969600000000000000$$ $$[2]$$ $$9437184$$ $$2.7567$$
273600.hj2 273600hj2 $$[0, 0, 0, -734700, -51086000]$$ $$14688124849/8122500$$ $$24253655040000000000$$ $$[2, 2]$$ $$4718592$$ $$2.4101$$
273600.hj3 273600hj1 $$[0, 0, 0, -446700, 114226000]$$ $$3301293169/22800$$ $$68080435200000000$$ $$[2]$$ $$2359296$$ $$2.0635$$ $$\Gamma_0(N)$$-optimal
273600.hj4 273600hj3 $$[0, 0, 0, 2865300, -403886000]$$ $$871257511151/527800050$$ $$-1576002504499200000000$$ $$[2]$$ $$9437184$$ $$2.7567$$

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 273600.hj do not have complex multiplication.

## 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.