# Properties

 Label 3150.x Number of curves $2$ Conductor $3150$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 3150.x

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3150.x1 3150bh2 $$[1, -1, 1, -410, 4587]$$ $$-417267265/235298$$ $$-4288306050$$ $$[]$$ $$2160$$ $$0.55144$$
3150.x2 3150bh1 $$[1, -1, 1, 40, -93]$$ $$397535/392$$ $$-7144200$$ $$[]$$ $$720$$ $$0.0021345$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 3150.x have rank $$1$$.

## Complex multiplication

The elliptic curves in class 3150.x do not have complex multiplication.

## Modular form3150.2.a.x

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} - q^{7} + q^{8} - 3 q^{11} - 2 q^{13} - q^{14} + q^{16} + 3 q^{17} - 7 q^{19} + O(q^{20})$$ ## 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. 