# Properties

 Label 390.g Number of curves $4$ Conductor $390$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("390.g1")

sage: E.isogeny_class()

## Elliptic curves in class 390.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
390.g1 390c4 [1, 0, 0, -1196, -15210]  288
390.g2 390c2 [1, 0, 0, -206, 1116]  96
390.g3 390c1 [1, 0, 0, -6, 36]  48 $$\Gamma_0(N)$$-optimal
390.g4 390c3 [1, 0, 0, 54, -960]  144

## Rank

sage: E.rank()

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

## Modular form390.2.a.g

sage: E.q_eigenform(10)

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

## 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 LMFDB numbering.

$$\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 