# Properties

 Label 235200ux Number of curves 8 Conductor 235200 CM no Rank 2 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("235200.ux1")

sage: E.isogeny_class()

## Elliptic curves in class 235200ux

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
235200.ux7 235200ux1 [0, 1, 0, -39005633, 93715660863] [2] 21233664 $$\Gamma_0(N)$$-optimal
235200.ux6 235200ux2 [0, 1, 0, -45277633, 61546572863] [2, 2] 42467328
235200.ux5 235200ux3 [0, 1, 0, -115445633, -362883979137] [2] 63700992
235200.ux8 235200ux4 [0, 1, 0, 150722367, 452174572863] [2] 84934656
235200.ux4 235200ux5 [0, 1, 0, -341629633, -2387802707137] [2] 84934656
235200.ux2 235200ux6 [0, 1, 0, -1721077633, -27480402827137] [2, 2] 127401984
235200.ux3 235200ux7 [0, 1, 0, -1595637633, -31655924107137] [2] 254803968
235200.ux1 235200ux8 [0, 1, 0, -27536629633, -1758800397707137] [2] 254803968

## Rank

sage: E.rank()

The elliptic curves in class 235200ux have rank $$2$$.

## Modular form 235200.2.a.ux

sage: E.q_eigenform(10)

$$q + q^{3} + q^{9} - 2q^{13} - 6q^{17} - 8q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.