# Properties

 Label 4560.i Number of curves $2$ Conductor $4560$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("i1")

sage: E.isogeny_class()

## Elliptic curves in class 4560.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4560.i1 4560o2 $$[0, -1, 0, -76, 76]$$ $$192143824/106875$$ $$27360000$$ $$$$ $$1536$$ $$0.11742$$
4560.i2 4560o1 $$[0, -1, 0, 19, 0]$$ $$44957696/27075$$ $$-433200$$ $$$$ $$768$$ $$-0.22916$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 4560.i have rank $$0$$.

## Complex multiplication

The elliptic curves in class 4560.i do not have complex multiplication.

## Modular form4560.2.a.i

sage: E.q_eigenform(10)

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