# Properties

 Label 4800cb Number of curves $6$ Conductor $4800$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("cb1")

sage: E.isogeny_class()

## Elliptic curves in class 4800cb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4800.cc5 4800cb1 $$[0, 1, 0, 67, -237]$$ $$2048/3$$ $$-48000000$$ $$[2]$$ $$1024$$ $$0.15937$$ $$\Gamma_0(N)$$-optimal
4800.cc4 4800cb2 $$[0, 1, 0, -433, -2737]$$ $$35152/9$$ $$2304000000$$ $$[2, 2]$$ $$2048$$ $$0.50594$$
4800.cc2 4800cb3 $$[0, 1, 0, -6433, -200737]$$ $$28756228/3$$ $$3072000000$$ $$[2]$$ $$4096$$ $$0.85251$$
4800.cc3 4800cb4 $$[0, 1, 0, -2433, 43263]$$ $$1556068/81$$ $$82944000000$$ $$[2, 2]$$ $$4096$$ $$0.85251$$
4800.cc1 4800cb5 $$[0, 1, 0, -38433, 2887263]$$ $$3065617154/9$$ $$18432000000$$ $$[2]$$ $$8192$$ $$1.1991$$
4800.cc6 4800cb6 $$[0, 1, 0, 1567, 175263]$$ $$207646/6561$$ $$-13436928000000$$ $$[2]$$ $$8192$$ $$1.1991$$

## Rank

sage: E.rank()

The elliptic curves in class 4800cb have rank $$1$$.

## Complex multiplication

The elliptic curves in class 4800cb do not have complex multiplication.

## Modular form4800.2.a.cb

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.