Properties

 Label 350064.br Number of curves $4$ Conductor $350064$ CM no Rank $1$ Graph

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

sage: E.isogeny_class()

Elliptic curves in class 350064.br

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
350064.br1 350064br3 $$[0, 0, 0, -474511755, -3977821865158]$$ $$3957101249824708884951625/772310238681366528$$ $$2306106015738741550743552$$ $$[2]$$ $$87588864$$ $$3.6745$$
350064.br2 350064br4 $$[0, 0, 0, -424376715, -4851184288966]$$ $$-2830680648734534916567625/1766676274677722124288$$ $$-5275267089367283419569979392$$ $$[2]$$ $$175177728$$ $$4.0211$$
350064.br3 350064br1 $$[0, 0, 0, -14446875, 13685927114]$$ $$111675519439697265625/37528570137307392$$ $$112059709972877675593728$$ $$[2]$$ $$29196288$$ $$3.1252$$ $$\Gamma_0(N)$$-optimal
350064.br4 350064br2 $$[0, 0, 0, 42150885, 94586765258]$$ $$2773679829880629422375/2899504554614368272$$ $$-8657874208005629830299648$$ $$[2]$$ $$58392576$$ $$3.4718$$

Rank

sage: E.rank()

The elliptic curves in class 350064.br have rank $$1$$.

Complex multiplication

The elliptic curves in class 350064.br do not have complex multiplication.

Modular form 350064.2.a.br

sage: E.q_eigenform(10)

$$q + 4 q^{7} + q^{11} + q^{13} - q^{17} - 2 q^{19} + O(q^{20})$$

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.