# Properties

 Label 14490.z Number of curves 8 Conductor 14490 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("14490.z1")
sage: E.isogeny_class()

## Elliptic curves in class 14490.z

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
14490.z1 14490bb7 [1, -1, 0, -2285091144, 39448430519400] 6 15925248
14490.z2 14490bb6 [1, -1, 0, -2245670064, 40961041011648] 12 7962624
14490.z3 14490bb3 [1, -1, 0, -2245667184, 40961151325440] 6 3981312
14490.z4 14490bb8 [1, -1, 0, -2206295064, 42466591386648] 6 15925248
14490.z5 14490bb4 [1, -1, 0, -425852784, -3370791981312] 2 5308416
14490.z6 14490bb2 [1, -1, 0, -39541104, 3795068160] 4 2654208
14490.z7 14490bb1 [1, -1, 0, -27744624, 56107738368] 2 1327104 $$\Gamma_0(N)$$-optimal
14490.z8 14490bb5 [1, -1, 0, 158026896, 30229666560] 2 5308416

## Rank

sage: E.rank()

The elliptic curves in class 14490.z have rank $$1$$.

## Modular form None

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

## 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.

$$\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 3 & 6 & 12 & 12 \\ 2 & 1 & 2 & 2 & 6 & 3 & 6 & 6 \\ 4 & 2 & 1 & 4 & 12 & 6 & 3 & 12 \\ 4 & 2 & 4 & 1 & 12 & 6 & 12 & 3 \\ 3 & 6 & 12 & 12 & 1 & 2 & 4 & 4 \\ 6 & 3 & 6 & 6 & 2 & 1 & 2 & 2 \\ 12 & 6 & 3 & 12 & 4 & 2 & 1 & 4 \\ 12 & 6 & 12 & 3 & 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.