# Properties

 Label 123200bf Number of curves 4 Conductor 123200 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("123200.t1")

sage: E.isogeny_class()

## Elliptic curves in class 123200bf

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
123200.t3 123200bf1 [0, 1, 0, -89633, 200972863] [2] 2654208 $$\Gamma_0(N)$$-optimal
123200.t2 123200bf2 [0, 1, 0, -5721633, 5219084863] [2] 5308416
123200.t4 123200bf3 [0, 1, 0, 806367, -5414259137] [2] 7962624
123200.t1 123200bf4 [0, 1, 0, -41785633, -101033299137] [2] 15925248

## Rank

sage: E.rank()

The elliptic curves in class 123200bf have rank $$0$$.

## Modular form 123200.2.a.t

sage: E.q_eigenform(10)

$$q - 2q^{3} - q^{7} + q^{9} + q^{11} - 4q^{13} + 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.