# Properties

 Label 95550bp Number of curves $6$ Conductor $95550$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("95550.cp1")

sage: E.isogeny_class()

## Elliptic curves in class 95550bp

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
95550.cp6 95550bp1 [1, 1, 0, 18350, -375500] [2] 589824 $$\Gamma_0(N)$$-optimal
95550.cp5 95550bp2 [1, 1, 0, -79650, -3217500] [2, 2] 1179648
95550.cp3 95550bp3 [1, 1, 0, -692150, 219120000] [2, 2] 2359296
95550.cp2 95550bp4 [1, 1, 0, -1035150, -405483000] [2] 2359296
95550.cp4 95550bp5 [1, 1, 0, -140900, 559241250] [2] 4718592
95550.cp1 95550bp6 [1, 1, 0, -11043400, 14120848750] [2] 4718592

## Rank

sage: E.rank()

The elliptic curves in class 95550bp have rank $$1$$.

## Modular form 95550.2.a.cp

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} + q^{6} - q^{8} + q^{9} + 4q^{11} - q^{12} + q^{13} + q^{16} - 6q^{17} - q^{18} - 4q^{19} + O(q^{20})$$

## 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 Cremona numbering.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.