# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("100014.c1")
sage: E.isogeny_class()

## Elliptic curves in class 100014.c

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
100014.c1 100014c2 [1, 1, 1, -1804, -29839] 2 73728
100014.c2 100014c1 [1, 1, 1, -224, 497] 2 36864 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form None

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.