# Properties

 Label 235200.cj Number of curves $6$ Conductor $235200$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("235200.cj1")

sage: E.isogeny_class()

## Elliptic curves in class 235200.cj

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
235200.cj1 235200cj6 [0, -1, 0, -51353633, -141625900863] [2] 18874368
235200.cj2 235200cj4 [0, -1, 0, -3333633, -2031760863] [2, 2] 9437184
235200.cj3 235200cj2 [0, -1, 0, -883633, 288389137] [2, 2] 4718592
235200.cj4 235200cj1 [0, -1, 0, -859133, 306788637] [2] 2359296 $$\Gamma_0(N)$$-optimal
235200.cj5 235200cj3 [0, -1, 0, 1174367, 1430579137] [2] 9437184
235200.cj6 235200cj5 [0, -1, 0, 5486367, -10966420863] [2] 18874368

## Rank

sage: E.rank()

The elliptic curves in class 235200.cj have rank $$1$$.

## Modular form 235200.2.a.cj

sage: E.q_eigenform(10)

$$q - q^{3} + q^{9} - 4q^{11} + 2q^{13} + 2q^{17} + 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.