# Properties

 Label 53900.b Number of curves $4$ Conductor $53900$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("b1")

sage: E.isogeny_class()

## Elliptic curves in class 53900.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
53900.b1 53900o4 [0, 1, 0, -8697908, 9870581188] [2] 1492992
53900.b2 53900o3 [0, 1, 0, -545533, 152950188] [2] 746496
53900.b3 53900o2 [0, 1, 0, -122908, 9331188] [2] 497664
53900.b4 53900o1 [0, 1, 0, -55533, -4952312] [2] 248832 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 53900.b have rank $$1$$.

## Complex multiplication

The elliptic curves in class 53900.b do not have complex multiplication.

## Modular form 53900.2.a.b

sage: E.q_eigenform(10)

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

## 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 LMFDB 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 LMFDB labels.