Properties

 Label 236992.k Number of curves $2$ Conductor $236992$ CM no Rank $0$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("k1")

sage: E.isogeny_class()

Elliptic curves in class 236992.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
236992.k1 236992k2 $$[0, 1, 0, -1151809, 461125695]$$ $$1431644/49$$ $$5783976700260319232$$ $$$$ $$3956736$$ $$2.3720$$
236992.k2 236992k1 $$[0, 1, 0, -178449, -19130129]$$ $$21296/7$$ $$206570596437868544$$ $$$$ $$1978368$$ $$2.0254$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 236992.k have rank $$0$$.

Complex multiplication

The elliptic curves in class 236992.k do not have complex multiplication.

Modular form 236992.2.a.k

sage: E.q_eigenform(10)

$$q - 2 q^{3} - 2 q^{5} + q^{7} + q^{9} + 2 q^{13} + 4 q^{15} + 2 q^{17} + 4 q^{19} + O(q^{20})$$ 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels. 