# Properties

 Label 4200o Number of curves $6$ Conductor $4200$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("4200.bb1")

sage: E.isogeny_class()

## Elliptic curves in class 4200o

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4200.bb4 4200o1 [0, 1, 0, -4383, 110238] [2] 3072 $$\Gamma_0(N)$$-optimal
4200.bb3 4200o2 [0, 1, 0, -4508, 103488] [2, 2] 6144
4200.bb2 4200o3 [0, 1, 0, -17008, -746512] [2, 2] 12288
4200.bb5 4200o4 [0, 1, 0, 5992, 523488] [2] 12288
4200.bb1 4200o5 [0, 1, 0, -262008, -51706512] [2] 24576
4200.bb6 4200o6 [0, 1, 0, 27992, -3986512] [2] 24576

## Rank

sage: E.rank()

The elliptic curves in class 4200o have rank $$1$$.

## Modular form4200.2.a.bb

sage: E.q_eigenform(10)

$$q + q^{3} + q^{7} + q^{9} - 4q^{11} + 2q^{13} - 2q^{17} - 4q^{19} + O(q^{20})$$

## 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.