# Properties

 Label 1296.k Number of curves $2$ Conductor $1296$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("k1")

sage: E.isogeny_class()

## Elliptic curves in class 1296.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1296.k1 1296f2 $$[0, 0, 0, -81, 243]$$ $$6912$$ $$8503056$$ $$[]$$ $$216$$ $$0.054953$$
1296.k2 1296f1 $$[0, 0, 0, -21, -37]$$ $$790272$$ $$1296$$ $$[]$$ $$72$$ $$-0.49435$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 1296.k have rank $$0$$.

## Complex multiplication

The elliptic curves in class 1296.k do not have complex multiplication.

## Modular form1296.2.a.k

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.