# Properties

 Label 161874.g Number of curves 6 Conductor 161874 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("161874.g1")

sage: E.isogeny_class()

## Elliptic curves in class 161874.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
161874.g1 161874bp6 [1, -1, 0, -132089283, -584285278581] [2] 12976128
161874.g2 161874bp4 [1, -1, 0, -8255673, -9127693575] [2, 2] 6488064
161874.g3 161874bp5 [1, -1, 0, -7827183, -10117762569] [2] 12976128
161874.g4 161874bp2 [1, -1, 0, -542853, -126832635] [2, 2] 3244032
161874.g5 161874bp1 [1, -1, 0, -161973, 23310261] [2] 1622016 $$\Gamma_0(N)$$-optimal
161874.g6 161874bp3 [1, -1, 0, 1075887, -739687599] [2] 6488064

## Rank

sage: E.rank()

The elliptic curves in class 161874.g have rank $$0$$.

## Modular form 161874.2.a.g

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - 2q^{5} - q^{8} + 2q^{10} - 4q^{11} - 2q^{13} + q^{16} + q^{17} - 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.