# Properties

 Label 100014.e Number of curves 2 Conductor 100014 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("100014.e1")
sage: E.isogeny_class()

## Elliptic curves in class 100014.e

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
100014.e1 100014f2 [1, 0, 0, -87037, -9623389] 1 1213920
100014.e2 100014f1 [1, 0, 0, -11707, 482009] 3 404640 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 100014.e have rank $$1$$.

## Modular form None

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

## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.