# Properties

 Label 119952gs Number of curves $6$ Conductor $119952$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("119952.bx1")

sage: E.isogeny_class()

## Elliptic curves in class 119952gs

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
119952.bx5 119952gs1 [0, 0, 0, -495641811, -4241860146286] [2] 35389440 $$\Gamma_0(N)$$-optimal
119952.bx4 119952gs2 [0, 0, 0, -640148691, -1566719882350] [2, 2] 70778880
119952.bx6 119952gs3 [0, 0, 0, 2469007149, -12322533595246] [2] 141557760
119952.bx2 119952gs4 [0, 0, 0, -6061414611, 180398070722450] [2, 2] 141557760
119952.bx3 119952gs5 [0, 0, 0, -2064613971, 414744081367826] [2] 283115520
119952.bx1 119952gs6 [0, 0, 0, -96798469971, 11591798658784274] [2] 283115520

## Rank

sage: E.rank()

The elliptic curves in class 119952gs have rank $$1$$.

## Modular form 119952.2.a.bx

sage: E.q_eigenform(10)

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

## 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 Cremona 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 Cremona labels.