# Properties

 Label 29645.h Number of curves $4$ Conductor $29645$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 29645.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
29645.h1 29645d4 $$[1, -1, 0, -60871190, 182810845531]$$ $$119678115308998401/1925$$ $$401213081671325$$ $$$$ $$1474560$$ $$2.8008$$
29645.h2 29645d3 $$[1, -1, 0, -4130660, 2338524425]$$ $$37397086385121/10316796875$$ $$2150251359582257421875$$ $$$$ $$1474560$$ $$2.8008$$
29645.h3 29645d2 $$[1, -1, 0, -3804565, 2856950256]$$ $$29220958012401/3705625$$ $$772335182217300625$$ $$[2, 2]$$ $$737280$$ $$2.4542$$
29645.h4 29645d1 $$[1, -1, 0, -217520, 52598475]$$ $$-5461074081/2562175$$ $$-534014611704533575$$ $$$$ $$368640$$ $$2.1077$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 29645.h have rank $$1$$.

## Complex multiplication

The elliptic curves in class 29645.h do not have complex multiplication.

## Modular form 29645.2.a.h

sage: E.q_eigenform(10)

$$q + q^{2} - q^{4} - q^{5} - 3q^{8} - 3q^{9} - q^{10} - 6q^{13} - q^{16} + 6q^{17} - 3q^{18} - 4q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 