# Properties

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

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("jh1")

sage: E.isogeny_class()

## Elliptic curves in class 273600jh

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
273600.jh3 273600jh1 $$[0, 0, 0, -446700, -114226000]$$ $$3301293169/22800$$ $$68080435200000000$$ $$[2]$$ $$2359296$$ $$2.0635$$ $$\Gamma_0(N)$$-optimal
273600.jh2 273600jh2 $$[0, 0, 0, -734700, 51086000]$$ $$14688124849/8122500$$ $$24253655040000000000$$ $$[2, 2]$$ $$4718592$$ $$2.4101$$
273600.jh1 273600jh3 $$[0, 0, 0, -8942700, 10278254000]$$ $$26487576322129/44531250$$ $$132969600000000000000$$ $$[2]$$ $$9437184$$ $$2.7567$$
273600.jh4 273600jh4 $$[0, 0, 0, 2865300, 403886000]$$ $$871257511151/527800050$$ $$-1576002504499200000000$$ $$[2]$$ $$9437184$$ $$2.7567$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 273600.2.a.jh

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 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.