# Properties

 Label 4800.cj Number of curves 4 Conductor 4800 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("4800.cj1")

sage: E.isogeny_class()

## Elliptic curves in class 4800.cj

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4800.cj1 4800cl4 [0, 1, 0, -52993, -4697857]  15360
4800.cj2 4800cl2 [0, 1, 0, -3393, 74943]  3072
4800.cj3 4800cl3 [0, 1, 0, -1793, -141057]  7680
4800.cj4 4800cl1 [0, 1, 0, -193, 1343]  1536 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form4800.2.a.cj

sage: E.q_eigenform(10)

$$q + q^{3} + 2q^{7} + q^{9} + 2q^{11} + 6q^{13} - 2q^{17} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 5 & 2 & 10 \\ 5 & 1 & 10 & 2 \\ 2 & 10 & 1 & 5 \\ 10 & 2 & 5 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 