# Properties

 Label 14994.u Number of curves 4 Conductor 14994 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("14994.u1")

sage: E.isogeny_class()

## Elliptic curves in class 14994.u

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
14994.u1 14994t4 [1, -1, 0, -49842, -2947190]  82944
14994.u2 14994t3 [1, -1, 0, -45432, -3715412]  41472
14994.u3 14994t2 [1, -1, 0, -18972, 1010344]  27648
14994.u4 14994t1 [1, -1, 0, -1332, 11920]  13824 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 14994.u have rank $$1$$.

## Modular form 14994.2.a.u

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - q^{8} - 6q^{11} - 2q^{13} + q^{16} - q^{17} + 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 