# Properties

 Label 126960.q Number of curves $6$ Conductor $126960$ CM no Rank $1$ Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("126960.q1")

sage: E.isogeny_class()

## Elliptic curves in class 126960.q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
126960.q1 126960ba4 [0, -1, 0, -934425776, 10994554397376] [4] 19464192
126960.q2 126960ba6 [0, -1, 0, -218625296, -1065715442880] [2] 38928384
126960.q3 126960ba3 [0, -1, 0, -59925296, 162368637120] [2, 2] 19464192
126960.q4 126960ba2 [0, -1, 0, -58401776, 171803491776] [2, 2] 9732096
126960.q5 126960ba1 [0, -1, 0, -3555056, 2831716800] [2] 4866048 $$\Gamma_0(N)$$-optimal
126960.q6 126960ba5 [0, -1, 0, 74398384, 786597642816] [2] 38928384

## Rank

sage: E.rank()

The elliptic curves in class 126960.q have rank $$1$$.

## Modular form 126960.2.a.q

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} + q^{9} + 4q^{11} - 2q^{13} + q^{15} + 6q^{17} + 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.