# Properties

 Label 95506.e Number of curves 4 Conductor 95506 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("95506.e1")

sage: E.isogeny_class()

## Elliptic curves in class 95506.e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
95506.e1 95506a4 [1, 1, 0, -317475, -47710717]  1797120
95506.e2 95506a3 [1, 1, 0, -289385, -60030991]  898560
95506.e3 95506a2 [1, 1, 0, -120845, 16115381]  599040
95506.e4 95506a1 [1, 1, 0, -8485, 182733]  299520 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 95506.e have rank $$1$$.

## Modular form 95506.2.a.e

sage: E.q_eigenform(10)

$$q - q^{2} + 2q^{3} + q^{4} - 2q^{6} - 4q^{7} - q^{8} + q^{9} + 6q^{11} + 2q^{12} + 2q^{13} + 4q^{14} + q^{16} - q^{17} - q^{18} + 4q^{19} + O(q^{20})$$

## 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 LMFDB 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 LMFDB labels. 