# Properties

 Label 3360.b Number of curves $2$ Conductor $3360$ CM no Rank $1$ Graph # Related objects

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

E.isogeny_class()

## Elliptic curves in class 3360.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3360.b1 3360a1 $$[0, -1, 0, -26, 60]$$ $$31554496/525$$ $$33600$$ $$$$ $$384$$ $$-0.33299$$ $$\Gamma_0(N)$$-optimal
3360.b2 3360a2 $$[0, -1, 0, -1, 145]$$ $$-64/2205$$ $$-9031680$$ $$$$ $$768$$ $$0.013582$$

## Rank

sage: E.rank()

The elliptic curves in class 3360.b have rank $$1$$.

## Complex multiplication

The elliptic curves in class 3360.b do not have complex multiplication.

## Modular form3360.2.a.b

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} - q^{7} + q^{9} - 2 q^{11} + q^{15} - 6 q^{17} + 6 q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 