# Properties

 Label 12480.z Number of curves $2$ Conductor $12480$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("z1")

sage: E.isogeny_class()

## Elliptic curves in class 12480.z

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
12480.z1 12480ch2 $$[0, -1, 0, -2945, 56097]$$ $$10779215329/1232010$$ $$322964029440$$ $$[2]$$ $$18432$$ $$0.94068$$
12480.z2 12480ch1 $$[0, -1, 0, 255, 4257]$$ $$6967871/35100$$ $$-9201254400$$ $$[2]$$ $$9216$$ $$0.59410$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 12480.2.a.z

sage: E.q_eigenform(10)

$$q - q^{3} + q^{5} - 2q^{7} + q^{9} + 4q^{11} + q^{13} - q^{15} + 8q^{17} - 6q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.