# Properties

 Label 171600.ge Number of curves $6$ Conductor $171600$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("171600.ge1")

sage: E.isogeny_class()

## Elliptic curves in class 171600.ge

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
171600.ge1 171600bs4 [0, 1, 0, -2745608, -1751995212] [2] 2097152
171600.ge2 171600bs5 [0, 1, 0, -1203608, 491752788] [2] 4194304
171600.ge3 171600bs3 [0, 1, 0, -189608, -21331212] [2, 2] 2097152
171600.ge4 171600bs2 [0, 1, 0, -171608, -27415212] [2, 2] 1048576
171600.ge5 171600bs1 [0, 1, 0, -9608, -523212] [2] 524288 $$\Gamma_0(N)$$-optimal
171600.ge6 171600bs6 [0, 1, 0, 536392, -144751212] [2] 4194304

## Rank

sage: E.rank()

The elliptic curves in class 171600.ge have rank $$0$$.

## Modular form 171600.2.a.ge

sage: E.q_eigenform(10)

$$q + q^{3} + q^{9} + q^{11} - q^{13} + 6q^{17} + 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.