# Properties

 Label 4800.p Number of curves $2$ Conductor $4800$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("p1")

sage: E.isogeny_class()

## Elliptic curves in class 4800.p

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4800.p1 4800bk2 $$[0, -1, 0, -4853, 131757]$$ $$-30866268160/3$$ $$-1228800$$ $$[]$$ $$3456$$ $$0.60179$$
4800.p2 4800bk1 $$[0, -1, 0, -53, 237]$$ $$-40960/27$$ $$-11059200$$ $$[]$$ $$1152$$ $$0.052484$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form4800.2.a.p

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. 