# Properties

 Label 259182.gd Number of curves $2$ Conductor $259182$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("gd1")

sage: E.isogeny_class()

## Elliptic curves in class 259182.gd

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
259182.gd1 259182gd1 $$[1, -1, 1, -221, 1829]$$ $$-13475473/7616$$ $$-671799744$$ $$[]$$ $$120960$$ $$0.39693$$ $$\Gamma_0(N)$$-optimal
259182.gd2 259182gd2 $$[1, -1, 1, 1759, -24307]$$ $$6827155247/6740636$$ $$-594584760924$$ $$[]$$ $$362880$$ $$0.94624$$

## Rank

sage: E.rank()

The elliptic curves in class 259182.gd have rank $$0$$.

## Complex multiplication

The elliptic curves in class 259182.gd do not have complex multiplication.

## Modular form 259182.2.a.gd

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + 3q^{5} - q^{7} + q^{8} + 3q^{10} + 4q^{13} - q^{14} + q^{16} - q^{17} + 4q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 