# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("j1")

sage: E.isogeny_class()

## Elliptic curves in class 30960.j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
30960.j1 30960r2 $$[0, 0, 0, -5163, -142758]$$ $$137627865747/36980$$ $$4089692160$$ $$$$ $$24576$$ $$0.82784$$
30960.j2 30960r1 $$[0, 0, 0, -363, -1638]$$ $$47832147/17200$$ $$1902182400$$ $$$$ $$12288$$ $$0.48127$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 30960.j have rank $$2$$.

## Complex multiplication

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

## Modular form 30960.2.a.j

sage: E.q_eigenform(10)

$$q - q^{5} - 6q^{13} - 2q^{17} - 2q^{19} + O(q^{20})$$ ## 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. 