# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("f1")

sage: E.isogeny_class()

## Elliptic curves in class 1792.f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1792.f1 1792e2 $$[0, -1, 0, -29, 5]$$ $$85184/49$$ $$1605632$$ $$$$ $$256$$ $$-0.11964$$
1792.f2 1792e1 $$[0, -1, 0, -19, 39]$$ $$1560896/7$$ $$3584$$ $$$$ $$128$$ $$-0.46622$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form1792.2.a.f

sage: E.q_eigenform(10)

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