# Properties

 Label 102850ce Number of curves 4 Conductor 102850 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("102850.di1")

sage: E.isogeny_class()

## Elliptic curves in class 102850ce

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
102850.di4 102850ce1 [1, 1, 1, -9138, -211969] [2] 311040 $$\Gamma_0(N)$$-optimal
102850.di3 102850ce2 [1, 1, 1, -130138, -18119969] [2] 622080
102850.di2 102850ce3 [1, 1, 1, -311638, 66822031] [2] 933120
102850.di1 102850ce4 [1, 1, 1, -341888, 53028031] [2] 1866240

## Rank

sage: E.rank()

The elliptic curves in class 102850ce have rank $$1$$.

## Modular form 102850.2.a.di

sage: E.q_eigenform(10)

$$q + q^{2} + 2q^{3} + q^{4} + 2q^{6} - 4q^{7} + q^{8} + q^{9} + 2q^{12} + 2q^{13} - 4q^{14} + q^{16} - q^{17} + q^{18} + 4q^{19} + O(q^{20})$$

## 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 Cremona 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 Cremona labels.