# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("h1")

sage: E.isogeny_class()

## Elliptic curves in class 1792.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1792.h1 1792d2 $$[0, -1, 0, -141, 533]$$ $$9528128/2401$$ $$78675968$$ $$$$ $$768$$ $$0.22494$$
1792.h2 1792d1 $$[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.h have rank $$0$$.

## Complex multiplication

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

## Modular form1792.2.a.h

sage: E.q_eigenform(10)

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