Properties

 Label 254100br Number of curves $4$ Conductor $254100$ CM no Rank $0$ Graph

Related objects

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

sage: E.isogeny_class()

Elliptic curves in class 254100br

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
254100.br3 254100br1 $$[0, -1, 0, -8050533, -8919520938]$$ $$-130287139815424/2250652635$$ $$-996792108178308750000$$ $$[2]$$ $$14929920$$ $$2.8272$$ $$\Gamma_0(N)$$-optimal
254100.br2 254100br2 $$[0, -1, 0, -129337908, -566113721688]$$ $$33766427105425744/9823275$$ $$69610123529100000000$$ $$[2]$$ $$29859840$$ $$3.1738$$
254100.br4 254100br3 $$[0, -1, 0, 31153467, -42767274438]$$ $$7549996227362816/6152409907875$$ $$-2724842362201235718750000$$ $$[2]$$ $$44789760$$ $$3.3765$$
254100.br1 254100br4 $$[0, -1, 0, -150028908, -372881561688]$$ $$52702650535889104/22020583921875$$ $$156043230692883187500000000$$ $$[2]$$ $$89579520$$ $$3.7231$$

Rank

sage: E.rank()

The elliptic curves in class 254100br have rank $$0$$.

Complex multiplication

The elliptic curves in class 254100br do not have complex multiplication.

Modular form 254100.2.a.br

sage: E.q_eigenform(10)

$$q - q^{3} + q^{7} + q^{9} + 2q^{13} - 6q^{17} - 8q^{19} + O(q^{20})$$

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.