# Properties

 Label 3360.q Number of curves $4$ Conductor $3360$ CM no Rank $0$ Graph

# Learn more

Show commands: SageMath
sage: E = EllipticCurve("q1")

sage: E.isogeny_class()

## Elliptic curves in class 3360.q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3360.q1 3360u2 $$[0, 1, 0, -324016, -71098216]$$ $$7347751505995469192/72930375$$ $$37340352000$$ $$[2]$$ $$15360$$ $$1.6049$$
3360.q2 3360u3 $$[0, 1, 0, -29016, -67716]$$ $$5276930158229192/3050936350875$$ $$1562079411648000$$ $$[2]$$ $$15360$$ $$1.6049$$
3360.q3 3360u1 $$[0, 1, 0, -20266, -1114216]$$ $$14383655824793536/45209390625$$ $$2893401000000$$ $$[2, 2]$$ $$7680$$ $$1.2583$$ $$\Gamma_0(N)$$-optimal
3360.q4 3360u4 $$[0, 1, 0, -11761, -2048065]$$ $$-43927191786304/415283203125$$ $$-1701000000000000$$ $$[2]$$ $$15360$$ $$1.6049$$

## Rank

sage: E.rank()

The elliptic curves in class 3360.q have rank $$0$$.

## Complex multiplication

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

## Modular form3360.2.a.q

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} + q^{7} + q^{9} - 4q^{11} - 2q^{13} - q^{15} - 2q^{17} + 4q^{19} + O(q^{20})$$

## 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.