# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("235200.bbn1")

sage: E.isogeny_class()

## Elliptic curves in class 235200bbn

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
235200.bbn4 235200bbn1 [0, 1, 0, -859133, -306788637] [2] 2359296 $$\Gamma_0(N)$$-optimal
235200.bbn3 235200bbn2 [0, 1, 0, -883633, -288389137] [2, 2] 4718592
235200.bbn2 235200bbn3 [0, 1, 0, -3333633, 2031760863] [2, 2] 9437184
235200.bbn5 235200bbn4 [0, 1, 0, 1174367, -1430579137] [2] 9437184
235200.bbn1 235200bbn5 [0, 1, 0, -51353633, 141625900863] [2] 18874368
235200.bbn6 235200bbn6 [0, 1, 0, 5486367, 10966420863] [2] 18874368

## Rank

sage: E.rank()

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

## Modular form 235200.2.a.bbn

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 Cremona numbering.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.