# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("bg1")

sage: E.isogeny_class()

## Elliptic curves in class 3150.bg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3150.bg1 3150br2 $$[1, -1, 1, -3155, 72947]$$ $$-7620530425/526848$$ $$-240045120000$$ $$$$ $$5184$$ $$0.93462$$
3150.bg2 3150br1 $$[1, -1, 1, 220, 47]$$ $$2595575/1512$$ $$-688905000$$ $$[]$$ $$1728$$ $$0.38532$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form3150.2.a.bg

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + q^{7} + q^{8} - 6q^{11} - q^{13} + q^{14} + q^{16} - 3q^{17} - 4q^{19} + O(q^{20})$$ ## 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. 