# Properties

 Label 390c Number of curves $4$ Conductor $390$ CM no Rank $0$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 390c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
390.g3 390c1 $$[1, 0, 0, -6, 36]$$ $$-24137569/561600$$ $$-561600$$ $$[6]$$ $$48$$ $$-0.21606$$ $$\Gamma_0(N)$$-optimal
390.g2 390c2 $$[1, 0, 0, -206, 1116]$$ $$967068262369/4928040$$ $$4928040$$ $$[6]$$ $$96$$ $$0.13052$$
390.g4 390c3 $$[1, 0, 0, 54, -960]$$ $$17394111071/411937500$$ $$-411937500$$ $$[2]$$ $$144$$ $$0.33325$$
390.g1 390c4 $$[1, 0, 0, -1196, -15210]$$ $$189208196468929/10860320250$$ $$10860320250$$ $$[2]$$ $$288$$ $$0.67982$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form390.2.a.c

sage: E.q_eigenform(10)

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

## 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 Cremona 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 Cremona labels.