# Properties

 Label 306.b Number of curves $6$ Conductor $306$ CM no Rank $0$ Graph

# Related objects

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

E.isogeny_class()

## Elliptic curves in class 306.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
306.b1 306c5 $$[1, -1, 0, -249696, 48087270]$$ $$2361739090258884097/5202$$ $$3792258$$ $$[2]$$ $$1024$$ $$1.3964$$
306.b2 306c3 $$[1, -1, 0, -15606, 754272]$$ $$576615941610337/27060804$$ $$19727326116$$ $$[2, 2]$$ $$512$$ $$1.0498$$
306.b3 306c6 $$[1, -1, 0, -14796, 835434]$$ $$-491411892194497/125563633938$$ $$-91535889140802$$ $$[2]$$ $$1024$$ $$1.3964$$
306.b4 306c2 $$[1, -1, 0, -1026, 10692]$$ $$163936758817/30338064$$ $$22116448656$$ $$[2, 2]$$ $$256$$ $$0.70324$$
306.b5 306c1 $$[1, -1, 0, -306, -1836]$$ $$4354703137/352512$$ $$256981248$$ $$[2]$$ $$128$$ $$0.35666$$ $$\Gamma_0(N)$$-optimal
306.b6 306c4 $$[1, -1, 0, 2034, 60264]$$ $$1276229915423/2927177028$$ $$-2133912053412$$ $$[2]$$ $$512$$ $$1.0498$$

## Rank

sage: E.rank()

The elliptic curves in class 306.b have rank $$0$$.

## Complex multiplication

The elliptic curves in class 306.b do not have complex multiplication.

## Modular form306.2.a.b

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.