# Properties

 Label 36300.y Number of curves $4$ Conductor $36300$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("y1")

sage: E.isogeny_class()

## Elliptic curves in class 36300.y

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
36300.y1 36300k4 $$[0, -1, 0, -756238908, 8004796890312]$$ $$6749703004355978704/5671875$$ $$40192290187500000000$$ $$[2]$$ $$4976640$$ $$3.4972$$
36300.y2 36300k3 $$[0, -1, 0, -47254533, 125144546562]$$ $$-26348629355659264/24169921875$$ $$-10704622741699218750000$$ $$[2]$$ $$2488320$$ $$3.1506$$
36300.y3 36300k2 $$[0, -1, 0, -9547908, 10459506312]$$ $$13584145739344/1195803675$$ $$8473756617146700000000$$ $$[2]$$ $$1658880$$ $$2.9479$$
36300.y4 36300k1 $$[0, -1, 0, 661467, 760600062]$$ $$72268906496/606436875$$ $$-268584979177968750000$$ $$[2]$$ $$829440$$ $$2.6013$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 36300.y have rank $$1$$.

## Complex multiplication

The elliptic curves in class 36300.y do not have complex multiplication.

## Modular form 36300.2.a.y

sage: E.q_eigenform(10)

$$q - q^{3} + 2q^{7} + q^{9} + 2q^{13} - 2q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.