# Properties

 Label 770.e Number of curves $2$ Conductor $770$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("e1")

sage: E.isogeny_class()

## Elliptic curves in class 770.e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
770.e1 770a2 $$[1, 1, 0, -73, -273]$$ $$43949604889/42350$$ $$42350$$ $$$$ $$128$$ $$-0.19101$$
770.e2 770a1 $$[1, 1, 0, -3, -7]$$ $$-4826809/10780$$ $$-10780$$ $$$$ $$64$$ $$-0.53759$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 770.e have rank $$0$$.

## Complex multiplication

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

## Modular form770.2.a.e

sage: E.q_eigenform(10)

$$q - q^{2} + 2 q^{3} + q^{4} - q^{5} - 2 q^{6} + q^{7} - q^{8} + q^{9} + q^{10} - q^{11} + 2 q^{12} + 2 q^{13} - q^{14} - 2 q^{15} + q^{16} + 2 q^{17} - q^{18} + 6 q^{19} + O(q^{20})$$ ## 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. 