# Properties

 Label 236992.ca Number of curves $2$ Conductor $236992$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("ca1")

sage: E.isogeny_class()

## Elliptic curves in class 236992.ca

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
236992.ca1 236992ca2 $$[0, -1, 0, -11934945, -15866079679]$$ $$38758598383688/25921$$ $$125738623918702592$$ $$$$ $$15138816$$ $$2.5974$$
236992.ca2 236992ca1 $$[0, -1, 0, -741305, -250951879]$$ $$-74299881664/1958887$$ $$-1187780929517744128$$ $$$$ $$7569408$$ $$2.2508$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 236992.ca have rank $$1$$.

## Complex multiplication

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

## Modular form 236992.2.a.ca

sage: E.q_eigenform(10)

$$q + 2q^{3} - 4q^{5} - q^{7} + q^{9} - 4q^{11} - 4q^{13} - 8q^{15} + 6q^{17} - 2q^{19} + O(q^{20})$$ ## 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. 