# Properties

 Label 4560.c Number of curves $4$ Conductor $4560$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("c1")

sage: E.isogeny_class()

## Elliptic curves in class 4560.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4560.c1 4560l4 $$[0, -1, 0, -36956, 2745900]$$ $$21804712949838544/8680921875$$ $$2222316000000$$ $$$$ $$13824$$ $$1.3331$$
4560.c2 4560l3 $$[0, -1, 0, -2661, 29736]$$ $$130287139815424/52926616125$$ $$846825858000$$ $$$$ $$6912$$ $$0.98648$$
4560.c3 4560l2 $$[0, -1, 0, -1316, -13284]$$ $$985329269584/252434475$$ $$64623225600$$ $$$$ $$4608$$ $$0.78375$$
4560.c4 4560l1 $$[0, -1, 0, -1221, -16020]$$ $$12592337649664/1315845$$ $$21053520$$ $$$$ $$2304$$ $$0.43718$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form4560.2.a.c

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 