# Properties

 Label 4560.m Number of curves $4$ Conductor $4560$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("m1")

sage: E.isogeny_class()

## Elliptic curves in class 4560.m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4560.m1 4560r4 $$[0, -1, 0, -119640, 15420912]$$ $$46237740924063961/1806561830400$$ $$7399677257318400$$ $$$$ $$20736$$ $$1.8122$$
4560.m2 4560r2 $$[0, -1, 0, -17640, -889488]$$ $$148212258825961/1218375000$$ $$4990464000000$$ $$$$ $$6912$$ $$1.2629$$
4560.m3 4560r1 $$[0, -1, 0, -360, -32400]$$ $$-1263214441/110808000$$ $$-453869568000$$ $$$$ $$3456$$ $$0.91637$$ $$\Gamma_0(N)$$-optimal
4560.m4 4560r3 $$[0, -1, 0, 3240, 871920]$$ $$918046641959/80912056320$$ $$-331415782686720$$ $$$$ $$10368$$ $$1.4657$$

## Rank

sage: E.rank()

The elliptic curves in class 4560.m have rank $$1$$.

## Complex multiplication

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

## Modular form4560.2.a.m

sage: E.q_eigenform(10)

$$q - q^{3} + q^{5} - 2 q^{7} + q^{9} + 2 q^{13} - q^{15} - q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 