# Properties

 Label 5202.c Number of curves 6 Conductor 5202 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("5202.c1")

sage: E.isogeny_class()

## Elliptic curves in class 5202.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
5202.c1 5202b5 [1, -1, 0, -72162198, 235964108794] [2] 294912
5202.c2 5202b3 [1, -1, 0, -4510188, 3687697660] [2, 2] 147456
5202.c3 5202b6 [1, -1, 0, -4276098, 4087382926] [2] 294912
5202.c4 5202b2 [1, -1, 0, -296568, 51343600] [2, 2] 73728
5202.c5 5202b1 [1, -1, 0, -88488, -9374144] [2] 36864 $$\Gamma_0(N)$$-optimal
5202.c6 5202b4 [1, -1, 0, 587772, 298428196] [2] 147456

## Rank

sage: E.rank()

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

## Modular form5202.2.a.c

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - 2q^{5} - q^{8} + 2q^{10} - 4q^{11} - 2q^{13} + q^{16} + 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.