# Properties

 Label 176400fn Number of curves 8 Conductor 176400 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("176400.lp1")

sage: E.isogeny_class()

## Elliptic curves in class 176400fn

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
176400.lp7 176400fn1 [0, 0, 0, -87762675, -316334236750] [2] 21233664 $$\Gamma_0(N)$$-optimal
176400.lp6 176400fn2 [0, 0, 0, -101874675, -207770620750] [2, 2] 42467328
176400.lp5 176400fn3 [0, 0, 0, -259752675, 1224603553250] [2] 63700992
176400.lp4 176400fn4 [0, 0, 0, -768666675, 8058449803250] [2] 84934656
176400.lp8 176400fn5 [0, 0, 0, 339125325, -1525919620750] [2] 84934656
176400.lp2 176400fn6 [0, 0, 0, -3872424675, 92744423329250] [2, 2] 127401984
176400.lp1 176400fn7 [0, 0, 0, -61957416675, 5935920363553250] [2] 254803968
176400.lp3 176400fn8 [0, 0, 0, -3590184675, 106836948769250] [2] 254803968

## Rank

sage: E.rank()

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

## Modular form 176400.2.a.lp

sage: E.q_eigenform(10)

$$q + 2q^{13} + 6q^{17} + 8q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.