# Properties

 Label 29645.e Number of curves $2$ Conductor $29645$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("e1")

sage: E.isogeny_class()

## Elliptic curves in class 29645.e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
29645.e1 29645n2 $$[1, 1, 1, -12797870, 1798487032]$$ $$835630707059/478515625$$ $$132745109443598544921875$$ $$$$ $$2534400$$ $$3.1266$$
29645.e2 29645n1 $$[1, 1, 1, 3180785, 226187380]$$ $$12829337821/7503125$$ $$-2081443316075625184375$$ $$$$ $$1267200$$ $$2.7800$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 29645.2.a.e

sage: E.q_eigenform(10)

$$q - q^{2} + 2q^{3} - q^{4} + q^{5} - 2q^{6} + 3q^{8} + q^{9} - q^{10} - 2q^{12} + 2q^{13} + 2q^{15} - q^{16} + 2q^{17} - q^{18} - 4q^{19} + O(q^{20})$$ ## 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. 