# Properties

 Label 13200.cu Number of curves 4 Conductor 13200 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("13200.cu1")

sage: E.isogeny_class()

## Elliptic curves in class 13200.cu

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
13200.cu1 13200bb3 [0, 1, 0, -17608, -905212] [2] 24576
13200.cu2 13200bb4 [0, 1, 0, -2608, 30788] [2] 24576
13200.cu3 13200bb2 [0, 1, 0, -1108, -14212] [2, 2] 12288
13200.cu4 13200bb1 [0, 1, 0, 17, -712] [2] 6144 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 13200.cu have rank $$1$$.

## Modular form 13200.2.a.cu

sage: E.q_eigenform(10)

$$q + q^{3} + 4q^{7} + q^{9} + q^{11} - 6q^{13} - 6q^{17} + 8q^{19} + O(q^{20})$$

## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.