# Properties

 Label 5929.h Number of curves 3 Conductor 5929 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("5929.h1")

sage: E.isogeny_class()

## Elliptic curves in class 5929.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
5929.h1 5929h3 [0, 1, 1, -46366756, -121538372763] [] 216000
5929.h2 5929h2 [0, 1, 1, -61266, -10592543] [] 43200
5929.h3 5929h1 [0, 1, 1, -1976, 79657] [] 8640 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 5929.h have rank $$1$$.

## Modular form5929.2.a.h

sage: E.q_eigenform(10)

$$q + 2q^{2} + q^{3} + 2q^{4} - q^{5} + 2q^{6} - 2q^{9} - 2q^{10} + 2q^{12} + 4q^{13} - q^{15} - 4q^{16} - 2q^{17} - 4q^{18} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 