# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("t1")

sage: E.isogeny_class()

## Elliptic curves in class 236992.t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
236992.t1 236992t2 $$[0, 1, 0, -5654657, -4899954977]$$ $$1030541881826/62236321$$ $$1207593744115219693568$$ $$$$ $$8110080$$ $$2.7977$$
236992.t2 236992t1 $$[0, 1, 0, -5570017, -5061634305]$$ $$1969910093092/7889$$ $$76536553689645056$$ $$$$ $$4055040$$ $$2.4511$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 236992.2.a.t

sage: E.q_eigenform(10)

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