# Properties

 Label 176400.lm Number of curves $8$ Conductor $176400$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("176400.lm1")

sage: E.isogeny_class()

## Elliptic curves in class 176400.lm

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
176400.lm1 176400fm8 [0, 0, 0, -1137960075, -9295716487750] [2] 127401984
176400.lm2 176400fm5 [0, 0, 0, -1016244075, -12469387099750] [2] 42467328
176400.lm3 176400fm6 [0, 0, 0, -476460075, 3896578012250] [2, 2] 63700992
176400.lm4 176400fm3 [0, 0, 0, -472932075, 3958639060250] [2] 31850496
176400.lm5 176400fm2 [0, 0, 0, -63684075, -193746379750] [2, 2] 21233664
176400.lm6 176400fm4 [0, 0, 0, -14292075, -486591547750] [2] 42467328
176400.lm7 176400fm1 [0, 0, 0, -7236075, 2636212250] [2] 10616832 $$\Gamma_0(N)$$-optimal
176400.lm8 176400fm7 [0, 0, 0, 128591925, 13116965440250] [2] 127401984

## Rank

sage: E.rank()

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

## Modular form 176400.2.a.lm

sage: E.q_eigenform(10)

$$q + 2q^{13} + 6q^{17} - 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.