# Properties

 Label 338130.x Number of curves $2$ Conductor $338130$ CM no Rank $0$ Graph # Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("x1")

sage: E.isogeny_class()

## Elliptic curves in class 338130.x

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
338130.x1 338130x1 $$[1, -1, 0, -2187495, 1245661821]$$ $$65787589563409/10400000$$ $$183001393130400000$$ $$$$ $$9830400$$ $$2.3229$$ $$\Gamma_0(N)$$-optimal
338130.x2 338130x2 $$[1, -1, 0, -1979415, 1491986925]$$ $$-48743122863889/26406250000$$ $$-464651974745156250000$$ $$$$ $$19660800$$ $$2.6694$$

## Rank

sage: E.rank()

The elliptic curves in class 338130.x have rank $$0$$.

## Complex multiplication

The elliptic curves in class 338130.x do not have complex multiplication.

## Modular form 338130.2.a.x

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - q^{5} + 4q^{7} - q^{8} + q^{10} - 2q^{11} - q^{13} - 4q^{14} + q^{16} + 6q^{19} + O(q^{20})$$ ## 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. 