# Properties

 Label 560.b Number of curves $3$ Conductor $560$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("b1")

sage: E.isogeny_class()

## Elliptic curves in class 560.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
560.b1 560c3 $$[0, -1, 0, -2101, 39485]$$ $$-250523582464/13671875$$ $$-56000000000$$ $$[]$$ $$432$$ $$0.82061$$
560.b2 560c1 $$[0, -1, 0, -21, -35]$$ $$-262144/35$$ $$-143360$$ $$[]$$ $$48$$ $$-0.27800$$ $$\Gamma_0(N)$$-optimal
560.b3 560c2 $$[0, -1, 0, 139, 61]$$ $$71991296/42875$$ $$-175616000$$ $$[]$$ $$144$$ $$0.27130$$

## Rank

sage: E.rank()

The elliptic curves in class 560.b have rank $$0$$.

## Complex multiplication

The elliptic curves in class 560.b do not have complex multiplication.

## Modular form560.2.a.b

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 