# Properties

 Label 116380e Number of curves $4$ Conductor $116380$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("e1")

sage: E.isogeny_class()

## Elliptic curves in class 116380e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
116380.a4 116380e1 [0, 1, 0, -23981, -1408100] [2] 427680 $$\Gamma_0(N)$$-optimal
116380.a3 116380e2 [0, 1, 0, -53076, 2641924] [2] 855360
116380.a2 116380e3 [0, 1, 0, -235581, 43377040] [2] 1283040
116380.a1 116380e4 [0, 1, 0, -3756076, 2800628724] [2] 2566080

## Rank

sage: E.rank()

The elliptic curves in class 116380e have rank $$0$$.

## Complex multiplication

The elliptic curves in class 116380e do not have complex multiplication.

## Modular form 116380.2.a.e

sage: E.q_eigenform(10)

$$q - 2q^{3} - q^{5} + 4q^{7} + q^{9} + q^{11} - 4q^{13} + 2q^{15} + 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.