# Properties

 Label 770.b Number of curves $2$ Conductor $770$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("b1")

sage: E.isogeny_class()

## Elliptic curves in class 770.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
770.b1 770d2 $$[1, 0, 1, -848, 9006]$$ $$67324767141241/3368750000$$ $$3368750000$$ $$$$ $$512$$ $$0.58688$$
770.b2 770d1 $$[1, 0, 1, 32, 558]$$ $$3789119879/135520000$$ $$-135520000$$ $$$$ $$256$$ $$0.24031$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 770.b have rank $$1$$.

## Complex multiplication

The elliptic curves in class 770.b do not have complex multiplication.

## Modular form770.2.a.b

sage: E.q_eigenform(10)

$$q - q^{2} - 2 q^{3} + q^{4} + q^{5} + 2 q^{6} - q^{7} - q^{8} + q^{9} - q^{10} + q^{11} - 2 q^{12} + q^{14} - 2 q^{15} + q^{16} - q^{18} + O(q^{20})$$ ## 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. 