# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("390.d1")

sage: E.isogeny_class()

## Elliptic curves in class 390.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
390.d1 390d4 [1, 0, 1, -872578, -313799212]  4320
390.d2 390d3 [1, 0, 1, -53378, -5124652]  2160
390.d3 390d2 [1, 0, 1, -16003, 27998]  1440
390.d4 390d1 [1, 0, 1, 3997, 3998]  720 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form390.2.a.d

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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 