# Properties

 Label 5202.d Number of curves 4 Conductor 5202 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("5202.d1")

sage: E.isogeny_class()

## Elliptic curves in class 5202.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
5202.d1 5202a4 [1, -1, 0, -293967, 42466387]  82944
5202.d2 5202a3 [1, -1, 0, -267957, 53447809]  41472
5202.d3 5202a2 [1, -1, 0, -111897, -14375867]  27648
5202.d4 5202a1 [1, -1, 0, -7857, -164003]  13824 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 5202.d have rank $$0$$.

## Modular form5202.2.a.d

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} + 4q^{7} - q^{8} + 6q^{11} + 2q^{13} - 4q^{14} + q^{16} - 4q^{19} + O(q^{20})$$

## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 