# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("390.c1")

sage: E.isogeny_class()

## Elliptic curves in class 390.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
390.c1 390g4 [1, 0, 1, -86529, 9789652]  1280
390.c2 390g3 [1, 0, 1, -6209, 104276]  1280
390.c3 390g2 [1, 0, 1, -5409, 152596] [2, 2] 640
390.c4 390g1 [1, 0, 1, -289, 3092]  320 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form390.2.a.c

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 