Properties

 Label 189618.br Number of curves $4$ Conductor $189618$ CM no Rank $0$ Graph

Related objects

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

sage: E.isogeny_class()

Elliptic curves in class 189618.br

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
189618.br1 189618j3 $$[1, 0, 0, -556892268, -5057497008240]$$ $$3957101249824708884951625/772310238681366528$$ $$3727794010859368089649152$$ $$[2]$$ $$76640256$$ $$3.7145$$
189618.br2 189618j4 $$[1, 0, 0, -498053228, -6167895603312]$$ $$-2830680648734534916567625/1766676274677722124288$$ $$-8527408942700901249012436992$$ $$[2]$$ $$153280512$$ $$4.0611$$
189618.br3 189618j1 $$[1, 0, 0, -16955013, 17399039553]$$ $$111675519439697265625/37528570137307392$$ $$181143240095886555472128$$ $$[2]$$ $$25546752$$ $$3.1652$$ $$\Gamma_0(N)$$-optimal
189618.br4 189618j2 $$[1, 0, 0, 49468747, 120262874289]$$ $$2773679829880629422375/2899504554614368272$$ $$-13995354679753624304604048$$ $$[2]$$ $$51093504$$ $$3.5118$$

Rank

sage: E.rank()

The elliptic curves in class 189618.br have rank $$0$$.

Complex multiplication

The elliptic curves in class 189618.br do not have complex multiplication.

Modular form 189618.2.a.br

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} + q^{6} + 4 q^{7} + q^{8} + q^{9} - q^{11} + q^{12} + 4 q^{14} + q^{16} + q^{17} + q^{18} - 2 q^{19} + O(q^{20})$$

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.