# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("390.b1")

sage: E.isogeny_class()

## Elliptic curves in class 390f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
390.b2 390f1 [1, 1, 0, -52, -176]  80 $$\Gamma_0(N)$$-optimal
390.b1 390f2 [1, 1, 0, -852, -9936]  160

## Rank

sage: E.rank()

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

## Modular form390.2.a.b

sage: E.q_eigenform(10)

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

## 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 Cremona 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 Cremona labels. 