# Properties

 Label 95830e Number of curves $4$ Conductor $95830$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("95830.j1")

sage: E.isogeny_class()

## Elliptic curves in class 95830e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
95830.j4 95830e1 [1, -1, 0, 3166, -110012]  193536 $$\Gamma_0(N)$$-optimal
95830.j3 95830e2 [1, -1, 0, -24214, -1166880] [2, 2] 387072
95830.j2 95830e3 [1, -1, 0, -120044, 14990058]  774144
95830.j1 95830e4 [1, -1, 0, -366464, -85291930]  774144

## Rank

sage: E.rank()

The elliptic curves in class 95830e have rank $$0$$.

## Modular form 95830.2.a.j

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} + q^{5} - q^{7} - q^{8} - 3q^{9} - q^{10} + 4q^{11} + 6q^{13} + q^{14} + q^{16} - 2q^{17} + 3q^{18} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 