# Properties

 Label 296450.gq Number of curves 4 Conductor 296450 CM no Rank 0 Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("296450.gq1")

sage: E.isogeny_class()

## Elliptic curves in class 296450.gq

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
296450.gq1 296450gq4 [1, 0, 0, -3871047188, -90075862264508] [2] 477757440
296450.gq2 296450gq2 [1, 0, 0, -530055688, 4655337028992] [2] 159252480
296450.gq3 296450gq1 [1, 0, 0, -8303688, 179226620992] [2] 79626240 $$\Gamma_0(N)$$-optimal
296450.gq4 296450gq3 [1, 0, 0, 74702312, -4827944317008] [2] 238878720

## Rank

sage: E.rank()

The elliptic curves in class 296450.gq have rank $$0$$.

## Modular form 296450.2.a.gq

sage: E.q_eigenform(10)

$$q + q^{2} - 2q^{3} + q^{4} - 2q^{6} + q^{8} + q^{9} - 2q^{12} + 4q^{13} + q^{16} + q^{18} - 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.