# Properties

 Label 176400.rj Number of curves $6$ Conductor $176400$ CM no Rank $0$ Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("176400.rj1")

sage: E.isogeny_class()

## Elliptic curves in class 176400.rj

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
176400.rj1 176400gp5 [0, 0, 0, -2963523675, 62095583898250] [2] 56623104
176400.rj2 176400gp3 [0, 0, 0, -185223675, 970205598250] [2, 2] 28311552
176400.rj3 176400gp6 [0, 0, 0, -172875675, 1105132194250] [2] 56623104
176400.rj4 176400gp4 [0, 0, 0, -65271675, -191839985750] [2] 28311552
176400.rj5 176400gp2 [0, 0, 0, -12351675, 13013334250] [2, 2] 14155776
176400.rj6 176400gp1 [0, 0, 0, 1760325, 1258038250] [2] 7077888 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 176400.rj have rank $$0$$.

## Modular form 176400.2.a.rj

sage: E.q_eigenform(10)

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

## 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 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.