# Properties

 Label 158400.nt Number of curves 4 Conductor 158400 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("158400.nt1")

sage: E.isogeny_class()

## Elliptic curves in class 158400.nt

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
158400.nt1 158400ni4 [0, 0, 0, -6390300, 6217702000] [2] 3981312
158400.nt2 158400ni3 [0, 0, 0, -400800, 96433000] [2] 1990656
158400.nt3 158400ni2 [0, 0, 0, -90300, 5902000] [2] 1327104
158400.nt4 158400ni1 [0, 0, 0, -40800, -3107000] [2] 663552 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 158400.nt have rank $$0$$.

## Modular form 158400.2.a.nt

sage: E.q_eigenform(10)

$$q + 4q^{7} - q^{11} - 4q^{13} + 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.