# Properties

 Label 1530.f Number of curves $4$ Conductor $1530$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
E = EllipticCurve("f1")

E.isogeny_class()

## Elliptic curves in class 1530.f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1530.f1 1530e4 $$[1, -1, 0, -1674, 26730]$$ $$711882749089/1721250$$ $$1254791250$$ $$$$ $$1024$$ $$0.62468$$
1530.f2 1530e3 $$[1, -1, 0, -1494, -21762]$$ $$506071034209/2505630$$ $$1826604270$$ $$$$ $$1024$$ $$0.62468$$
1530.f3 1530e2 $$[1, -1, 0, -144, 108]$$ $$454756609/260100$$ $$189612900$$ $$[2, 2]$$ $$512$$ $$0.27811$$
1530.f4 1530e1 $$[1, -1, 0, 36, 0]$$ $$6967871/4080$$ $$-2974320$$ $$$$ $$256$$ $$-0.068467$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 1530.f have rank $$1$$.

## Complex multiplication

The elliptic curves in class 1530.f do not have complex multiplication.

## Modular form1530.2.a.f

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} + q^{5} - q^{8} - q^{10} - 4 q^{11} + 2 q^{13} + q^{16} - q^{17} - 4 q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 