# Properties

 Label 22848.bc Number of curves $6$ Conductor $22848$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("22848.bc1")

sage: E.isogeny_class()

## Elliptic curves in class 22848.bc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
22848.bc1 22848bx6 [0, -1, 0, -877990657, 10013724179617] [4] 5898240
22848.bc2 22848bx4 [0, -1, 0, -54978817, 155852962465] [2, 2] 2949120
22848.bc3 22848bx5 [0, -1, 0, -18726657, 358277773473] [2] 5898240
22848.bc4 22848bx2 [0, -1, 0, -5806337, -1351456095] [2, 2] 1474560
22848.bc5 22848bx1 [0, -1, 0, -4495617, -3662779743] [2] 737280 $$\Gamma_0(N)$$-optimal
22848.bc6 22848bx3 [0, -1, 0, 22394623, -10652132703] [2] 2949120

## Rank

sage: E.rank()

The elliptic curves in class 22848.bc have rank $$1$$.

## Modular form 22848.2.a.bc

sage: E.q_eigenform(10)

$$q - q^{3} + 2q^{5} - q^{7} + q^{9} + 4q^{11} + 2q^{13} - 2q^{15} + q^{17} + 4q^{19} + O(q^{20})$$

## 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 LMFDB numbering.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.