# Properties

 Label 390.b Number of curves $2$ Conductor $390$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
E = EllipticCurve("b1")

E.isogeny_class()

## Elliptic curves in class 390.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
390.b1 390f2 $$[1, 1, 0, -852, -9936]$$ $$68523370149961/243360$$ $$243360$$ $$$$ $$160$$ $$0.25184$$
390.b2 390f1 $$[1, 1, 0, -52, -176]$$ $$-16022066761/998400$$ $$-998400$$ $$$$ $$80$$ $$-0.094738$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 390.b have rank $$0$$.

## Complex multiplication

The elliptic curves in class 390.b do not have complex multiplication.

## Modular form390.2.a.b

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} - 2 q^{7} - q^{8} + q^{9} - q^{10} + 4 q^{11} - q^{12} - q^{13} + 2 q^{14} - q^{15} + q^{16} + 4 q^{17} - q^{18} - 2 q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 