# Properties

 Label 1440.k Number of curves $4$ Conductor $1440$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 1440.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1440.k1 1440k3 $$[0, 0, 0, -732, 7616]$$ $$14526784/15$$ $$44789760$$ $$$$ $$512$$ $$0.38604$$
1440.k2 1440k2 $$[0, 0, 0, -507, -4354]$$ $$38614472/405$$ $$151165440$$ $$$$ $$512$$ $$0.38604$$
1440.k3 1440k1 $$[0, 0, 0, -57, 56]$$ $$438976/225$$ $$10497600$$ $$[2, 2]$$ $$256$$ $$0.039465$$ $$\Gamma_0(N)$$-optimal
1440.k4 1440k4 $$[0, 0, 0, 213, 434]$$ $$2863288/1875$$ $$-699840000$$ $$$$ $$512$$ $$0.38604$$

## Rank

sage: E.rank()

The elliptic curves in class 1440.k have rank $$0$$.

## Complex multiplication

The elliptic curves in class 1440.k do not have complex multiplication.

## Modular form1440.2.a.k

sage: E.q_eigenform(10)

$$q + q^{5} + 4q^{11} + 2q^{13} + 2q^{17} - 8q^{19} + O(q^{20})$$ ## 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. 