# Properties

 Label 1792.d Number of curves $2$ Conductor $1792$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("d1")

sage: E.isogeny_class()

## Elliptic curves in class 1792.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1792.d1 1792f2 $$[0, 1, 0, -141, -533]$$ $$9528128/2401$$ $$78675968$$ $$$$ $$768$$ $$0.22494$$
1792.d2 1792f1 $$[0, 1, 0, -131, -623]$$ $$489303872/49$$ $$25088$$ $$$$ $$384$$ $$-0.12163$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 1792.d have rank $$0$$.

## Complex multiplication

The elliptic curves in class 1792.d do not have complex multiplication.

## Modular form1792.2.a.d

sage: E.q_eigenform(10)

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