# Properties

 Label 102921.l Number of curves $6$ Conductor $102921$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("102921.l1")

sage: E.isogeny_class()

## Elliptic curves in class 102921.l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
102921.l1 102921e4 [1, 1, 0, -34581459, 78258791538] [2] 3538944
102921.l2 102921e6 [1, 1, 0, -7177264, -6019352867] [2] 7077888
102921.l3 102921e3 [1, 1, 0, -2202749, 1172800920] [2, 2] 3538944
102921.l4 102921e2 [1, 1, 0, -2161344, 1222114275] [2, 2] 1769472
102921.l5 102921e1 [1, 1, 0, -132499, 19820728] [2] 884736 $$\Gamma_0(N)$$-optimal
102921.l6 102921e5 [1, 1, 0, 2109286, 5209728087] [2] 7077888

## Rank

sage: E.rank()

The elliptic curves in class 102921.l have rank $$0$$.

## Modular form 102921.2.a.l

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} - q^{4} + 2q^{5} - q^{6} - q^{7} - 3q^{8} + q^{9} + 2q^{10} - 4q^{11} + q^{12} - q^{14} - 2q^{15} - q^{16} + 2q^{17} + q^{18} + 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.