Properties

 Label 161700br Number of curves $2$ Conductor $161700$ CM no Rank $0$ Graph Related objects

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

sage: E.isogeny_class()

Elliptic curves in class 161700br

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
161700.dd2 161700br1 $$[0, 1, 0, -100843633, 535048768988]$$ $$-3856034557002072064/1973796785296875$$ $$-58053804498348011718750000$$ $$$$ $$46448640$$ $$3.6483$$ $$\Gamma_0(N)$$-optimal
161700.dd1 161700br2 $$[0, 1, 0, -1775265508, 28785894643988]$$ $$1314817350433665559504/190690249278375$$ $$89738068549406161500000000$$ $$$$ $$92897280$$ $$3.9949$$

Rank

sage: E.rank()

The elliptic curves in class 161700br have rank $$0$$.

Complex multiplication

The elliptic curves in class 161700br do not have complex multiplication.

Modular form 161700.2.a.br

sage: E.q_eigenform(10)

$$q + q^{3} + q^{9} - q^{11} - 2 q^{17} + 6 q^{19} + O(q^{20})$$ 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 Cremona numbering.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with Cremona labels. 