# Properties

 Label 100011.d Number of curves 2 Conductor 100011 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("100011.d1")
sage: E.isogeny_class()

## Elliptic curves in class 100011.d

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
100011.d1 100011d1 [1, 0, 1, -692, 6941] 2 45312 $$\Gamma_0(N)$$-optimal
100011.d2 100011d2 [1, 0, 1, -647, 7895] 2 90624

## Rank

sage: E.rank()

The elliptic curves in class 100011.d have rank $$1$$.

## Modular form None

sage: E.q_eigenform(10)
$$q + q^{2} + q^{3} - q^{4} - 2q^{5} + q^{6} + 2q^{7} - 3q^{8} + q^{9} - 2q^{10} - 6q^{11} - q^{12} + 2q^{13} + 2q^{14} - 2q^{15} - q^{16} - q^{17} + q^{18} - 8q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.