# Properties

 Label 30960.k Number of curves $2$ Conductor $30960$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 30960.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
30960.k1 30960bj2 $$[0, 0, 0, -73083, -7602518]$$ $$14457238157881/4437600$$ $$13250602598400$$ $$$$ $$92160$$ $$1.4948$$
30960.k2 30960bj1 $$[0, 0, 0, -3963, -151382]$$ $$-2305199161/1981440$$ $$-5916548136960$$ $$$$ $$46080$$ $$1.1482$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 30960.k have rank $$0$$.

## Complex multiplication

The elliptic curves in class 30960.k do not have complex multiplication.

## Modular form 30960.2.a.k

sage: E.q_eigenform(10)

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

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 