# Properties

 Label 784.d Number of curves $2$ Conductor $784$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 784.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
784.d1 784g2 $$[0, -1, 0, -6974, 226507]$$ $$406749952$$ $$92236816$$ $$[]$$ $$504$$ $$0.76792$$
784.d2 784g1 $$[0, -1, 0, -114, 127]$$ $$1792$$ $$92236816$$ $$[]$$ $$168$$ $$0.21861$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 784.d have rank $$0$$.

## Complex multiplication

The elliptic curves in class 784.d do not have complex multiplication.

## Modular form784.2.a.d

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels. 