# Properties

 Label 14157.f Number of curves $6$ Conductor $14157$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("14157.f1")

sage: E.isogeny_class()

## Elliptic curves in class 14157.f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
14157.f1 14157l4 [1, -1, 1, -7474919, 7867939016] [2] 245760
14157.f2 14157l5 [1, -1, 1, -3276824, -2209998040] [2] 491520
14157.f3 14157l3 [1, -1, 1, -516209, 95667608] [2, 2] 245760
14157.f4 14157l2 [1, -1, 1, -467204, 123012398] [2, 2] 122880
14157.f5 14157l1 [1, -1, 1, -26159, 2342486] [2] 61440 $$\Gamma_0(N)$$-optimal
14157.f6 14157l6 [1, -1, 1, 1460326, 650678636] [2] 491520

## Rank

sage: E.rank()

The elliptic curves in class 14157.f have rank $$1$$.

## Modular form 14157.2.a.f

sage: E.q_eigenform(10)

$$q - q^{2} - q^{4} + 2q^{5} + 3q^{8} - 2q^{10} - q^{13} - q^{16} - 6q^{17} + 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.