# Properties

 Label 145200br Number of curves $4$ Conductor $145200$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("br1")

sage: E.isogeny_class()

## Elliptic curves in class 145200br

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
145200.hf4 145200br1 $$[0, 1, 0, 661467, -760600062]$$ $$72268906496/606436875$$ $$-268584979177968750000$$ $$[2]$$ $$3317760$$ $$2.6013$$ $$\Gamma_0(N)$$-optimal
145200.hf3 145200br2 $$[0, 1, 0, -9547908, -10459506312]$$ $$13584145739344/1195803675$$ $$8473756617146700000000$$ $$[2]$$ $$6635520$$ $$2.9479$$
145200.hf2 145200br3 $$[0, 1, 0, -47254533, -125144546562]$$ $$-26348629355659264/24169921875$$ $$-10704622741699218750000$$ $$[2]$$ $$9953280$$ $$3.1506$$
145200.hf1 145200br4 $$[0, 1, 0, -756238908, -8004796890312]$$ $$6749703004355978704/5671875$$ $$40192290187500000000$$ $$[2]$$ $$19906560$$ $$3.4972$$

## Rank

sage: E.rank()

The elliptic curves in class 145200br have rank $$0$$.

## Complex multiplication

The elliptic curves in class 145200br do not have complex multiplication.

## Modular form 145200.2.a.br

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 Cremona 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 Cremona labels.