# Properties

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

# Related objects

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

E.isogeny_class()

## Elliptic curves in class 3360q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3360.h3 3360q1 $$[0, -1, 0, -6378750, 6202979352]$$ $$448487713888272974160064/91549016015625$$ $$5859137025000000$$ $$[2, 2]$$ $$107520$$ $$2.4134$$ $$\Gamma_0(N)$$-optimal
3360.h2 3360q2 $$[0, -1, 0, -6400625, 6158314977]$$ $$7079962908642659949376/100085966990454375$$ $$409952120792901120000$$ $$[2]$$ $$215040$$ $$2.7600$$
3360.h1 3360q3 $$[0, -1, 0, -102060000, 396888659352]$$ $$229625675762164624948320008/9568125$$ $$4898880000$$ $$[2]$$ $$215040$$ $$2.7600$$
3360.h4 3360q4 $$[0, -1, 0, -6356880, 6247602900]$$ $$-55486311952875723077768/801237030029296875$$ $$-410233359375000000000$$ $$[4]$$ $$215040$$ $$2.7600$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form3360.2.a.q

sage: E.q_eigenform(10)

$$q - q^{3} + q^{5} + q^{7} + q^{9} - 4 q^{11} - 6 q^{13} - q^{15} + 6 q^{17} - 4 q^{19} + O(q^{20})$$

## 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 Cremona numbering.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.