# Properties

 Label 4800.cf Number of curves $2$ Conductor $4800$ CM no Rank $0$ Graph # Learn more

Show commands for: SageMath
sage: E = EllipticCurve("cf1")

sage: E.isogeny_class()

## Elliptic curves in class 4800.cf

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4800.cf1 4800ci2 $$[0, 1, 0, -121333, 16226963]$$ $$-30866268160/3$$ $$-19200000000$$ $$[]$$ $$17280$$ $$1.4065$$
4800.cf2 4800ci1 $$[0, 1, 0, -1333, 26963]$$ $$-40960/27$$ $$-172800000000$$ $$[]$$ $$5760$$ $$0.85720$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form4800.2.a.cf

sage: E.q_eigenform(10)

$$q + q^{3} + q^{7} + q^{9} + 6q^{11} - 5q^{13} - 6q^{17} + 5q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 