# Properties

 Label 14440h Number of curves 4 Conductor 14440 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("14440.g1")

sage: E.isogeny_class()

## Elliptic curves in class 14440h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
14440.g3 14440h1 [0, 0, 0, -722, -6859] [2] 6912 $$\Gamma_0(N)$$-optimal
14440.g2 14440h2 [0, 0, 0, -2527, 41154] [2, 2] 13824
14440.g1 14440h3 [0, 0, 0, -38627, 2921934] [2] 27648
14440.g4 14440h4 [0, 0, 0, 4693, 233206] [2] 27648

## Rank

sage: E.rank()

The elliptic curves in class 14440h have rank $$0$$.

## Modular form 14440.2.a.g

sage: E.q_eigenform(10)

$$q + q^{5} - 4q^{7} - 3q^{9} + 4q^{11} + 2q^{13} + 2q^{17} + O(q^{20})$$

## 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 Cremona numbering.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.