# Properties

 Label 177870.eb Number of curves 4 Conductor 177870 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("177870.eb1")

sage: E.isogeny_class()

## Elliptic curves in class 177870.eb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
177870.eb1 177870fj3 [1, 0, 1, -195603763, 1052935718888]  35389440
177870.eb2 177870fj2 [1, 0, 1, -12575533, 15458499956] [2, 2] 17694720
177870.eb3 177870fj1 [1, 0, 1, -2970553, -1711362292]  8847360 $$\Gamma_0(N)$$-optimal
177870.eb4 177870fj4 [1, 0, 1, 16773017, 76890884816]  35389440

## Rank

sage: E.rank()

The elliptic curves in class 177870.eb have rank $$1$$.

## Modular form 177870.2.a.eb

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 