# Properties

 Label 195195ca Number of curves $6$ Conductor $195195$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("195195.bl1")

sage: E.isogeny_class()

## Elliptic curves in class 195195ca

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
195195.bl4 195195ca1 [1, 1, 0, -44788, 3629683] [2] 589824 $$\Gamma_0(N)$$-optimal
195195.bl3 195195ca2 [1, 1, 0, -45633, 3484512] [2, 2] 1179648
195195.bl5 195195ca3 [1, 1, 0, 43092, 15497877] [2] 2359296
195195.bl2 195195ca4 [1, 1, 0, -147878, -17802897] [2, 2] 2359296
195195.bl6 195195ca5 [1, 1, 0, 307577, -105341348] [2] 4718592
195195.bl1 195195ca6 [1, 1, 0, -2239253, -1290613722] [2] 4718592

## Rank

sage: E.rank()

The elliptic curves in class 195195ca have rank $$0$$.

## Modular form 195195.2.a.bl

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} - q^{4} - q^{5} - q^{6} + q^{7} - 3q^{8} + q^{9} - q^{10} - q^{11} + q^{12} + q^{14} + q^{15} - q^{16} - 6q^{17} + q^{18} + 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.