# Properties

 Label 29645.a Number of curves $2$ Conductor $29645$ CM no Rank $2$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("a1")

sage: E.isogeny_class()

## Elliptic curves in class 29645.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
29645.a1 29645b2 $$[1, -1, 1, -3268, 69556]$$ $$24642171/1225$$ $$191823753275$$ $$$$ $$27648$$ $$0.92394$$
29645.a2 29645b1 $$[1, -1, 1, -573, -3748]$$ $$132651/35$$ $$5480678665$$ $$$$ $$13824$$ $$0.57736$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 29645.a have rank $$2$$.

## Complex multiplication

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

## Modular form 29645.2.a.a

sage: E.q_eigenform(10)

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

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 