# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("177600.ci1")

sage: E.isogeny_class()

## Elliptic curves in class 177600ir

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
177600.ci5 177600ir1 [0, -1, 0, -1352033, 2083475937] [2] 7962624 $$\Gamma_0(N)$$-optimal
177600.ci4 177600ir2 [0, -1, 0, -34120033, 76565139937] [2, 2] 15925248
177600.ci1 177600ir3 [0, -1, 0, -545608033, 4905523347937] [2] 31850496
177600.ci3 177600ir4 [0, -1, 0, -46920033, 13909139937] [2, 2] 31850496
177600.ci6 177600ir5 [0, -1, 0, 186359967, 110720339937] [4] 63700992
177600.ci2 177600ir6 [0, -1, 0, -485000033, -4093090860063] [2] 63700992

## Rank

sage: E.rank()

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

## Modular form 177600.2.a.ci

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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.