# Properties

 Label 177870.cp Number of curves $6$ Conductor $177870$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("177870.cp1")

sage: E.isogeny_class()

## Elliptic curves in class 177870.cp

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
177870.cp1 177870ge6 [1, 0, 1, -99607324, -382643588428]  15728640
177870.cp2 177870ge4 [1, 0, 1, -6225574, -5978961628] [2, 2] 7864320
177870.cp3 177870ge5 [1, 0, 1, -5810544, -6810349724]  15728640
177870.cp4 177870ge3 [1, 0, 1, -2193854, 1181942276]  7864320
177870.cp5 177870ge2 [1, 0, 1, -415154, -80223244] [2, 2] 3932160
177870.cp6 177870ge1 [1, 0, 1, 59166, -7747148]  1966080 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 177870.cp have rank $$0$$.

## Modular form 177870.2.a.cp

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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 8 & 4 & 8 \\ 8 & 4 & 8 & 1 & 2 & 4 \\ 4 & 2 & 4 & 2 & 1 & 2 \\ 8 & 4 & 8 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 