# Properties

 Label 1792.c Number of curves $2$ Conductor $1792$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("c1")

sage: E.isogeny_class()

## Elliptic curves in class 1792.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1792.c1 1792b2 $$[0, 1, 0, -77, 235]$$ $$1560896/7$$ $$229376$$ $$$$ $$256$$ $$-0.11964$$
1792.c2 1792b1 $$[0, 1, 0, -7, -3]$$ $$85184/49$$ $$25088$$ $$$$ $$128$$ $$-0.46622$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 1792.c have rank $$1$$.

## Complex multiplication

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

## Modular form1792.2.a.c

sage: E.q_eigenform(10)

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