# Properties

 Label 4800bp Number of curves 8 Conductor 4800 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("4800.d1")

sage: E.isogeny_class()

## Elliptic curves in class 4800bp

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4800.d8 4800bp1 [0, -1, 0, 2367, -136863] [2] 9216 $$\Gamma_0(N)$$-optimal
4800.d6 4800bp2 [0, -1, 0, -29633, -1768863] [2, 2] 18432
4800.d7 4800bp3 [0, -1, 0, -21633, 4015137] [2] 27648
4800.d4 4800bp4 [0, -1, 0, -461633, -120568863] [2] 36864
4800.d5 4800bp5 [0, -1, 0, -109633, 12071137] [2] 36864
4800.d3 4800bp6 [0, -1, 0, -533633, 149935137] [2, 2] 55296
4800.d2 4800bp7 [0, -1, 0, -725633, 32623137] [2] 110592
4800.d1 4800bp8 [0, -1, 0, -8533633, 9597935137] [2] 110592

## Rank

sage: E.rank()

The elliptic curves in class 4800bp have rank $$0$$.

## Modular form4800.2.a.d

sage: E.q_eigenform(10)

$$q - q^{3} - 4q^{7} + q^{9} + 2q^{13} - 6q^{17} - 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.