# Properties

 Label 12480.cx Number of curves $4$ Conductor $12480$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("cx1")

sage: E.isogeny_class()

## Elliptic curves in class 12480.cx

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
12480.cx1 12480bh3 $$[0, 1, 0, -865, -8257]$$ $$2186875592/428415$$ $$14038302720$$ $$[2]$$ $$6144$$ $$0.66378$$
12480.cx2 12480bh2 $$[0, 1, 0, -265, 1463]$$ $$504358336/38025$$ $$155750400$$ $$[2, 2]$$ $$3072$$ $$0.31720$$
12480.cx3 12480bh1 $$[0, 1, 0, -260, 1530]$$ $$30488290624/195$$ $$12480$$ $$[2]$$ $$1536$$ $$-0.029371$$ $$\Gamma_0(N)$$-optimal
12480.cx4 12480bh4 $$[0, 1, 0, 255, 6975]$$ $$55742968/658125$$ $$-21565440000$$ $$[4]$$ $$6144$$ $$0.66378$$

## Rank

sage: E.rank()

The elliptic curves in class 12480.cx have rank $$0$$.

## Complex multiplication

The elliptic curves in class 12480.cx do not have complex multiplication.

## Modular form 12480.2.a.cx

sage: E.q_eigenform(10)

$$q + q^{3} + q^{5} + q^{9} + q^{13} + q^{15} + 2 q^{17} + 4 q^{19} + O(q^{20})$$

## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.