# Properties

 Label 235200.r Number of curves 4 Conductor 235200 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("235200.r1")

sage: E.isogeny_class()

## Elliptic curves in class 235200.r

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
235200.r1 235200r3 [0, -1, 0, -1476533, 638332437] [2] 7962624
235200.r2 235200r1 [0, -1, 0, -300533, -63151563] [2] 2654208 $$\Gamma_0(N)$$-optimal
235200.r3 235200r2 [0, -1, 0, -178033, -115214063] [2] 5308416
235200.r4 235200r4 [0, -1, 0, 1585967, 2938269937] [2] 15925248

## Rank

sage: E.rank()

The elliptic curves in class 235200.r have rank $$0$$.

## Modular form 235200.2.a.r

sage: E.q_eigenform(10)

$$q - q^{3} + q^{9} - 6q^{11} + 4q^{13} + 6q^{17} + 2q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.