# Properties

 Label 177600bp Number of curves $6$ Conductor $177600$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("177600.hd1")

sage: E.isogeny_class()

## Elliptic curves in class 177600bp

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
177600.hd5 177600bp1 [0, 1, 0, -1352033, -2083475937] [2] 7962624 $$\Gamma_0(N)$$-optimal
177600.hd4 177600bp2 [0, 1, 0, -34120033, -76565139937] [2, 2] 15925248
177600.hd3 177600bp3 [0, 1, 0, -46920033, -13909139937] [2, 2] 31850496
177600.hd1 177600bp4 [0, 1, 0, -545608033, -4905523347937] [2] 31850496
177600.hd2 177600bp5 [0, 1, 0, -485000033, 4093090860063] [4] 63700992
177600.hd6 177600bp6 [0, 1, 0, 186359967, -110720339937] [2] 63700992

## Rank

sage: E.rank()

The elliptic curves in class 177600bp have rank $$0$$.

## Modular form 177600.2.a.hd

sage: E.q_eigenform(10)

$$q + q^{3} + q^{9} + 4q^{11} - 2q^{13} - 2q^{17} + 4q^{19} + O(q^{20})$$

## 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 Cremona numbering.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.