# Properties

 Label 3366.c Number of curves $2$ Conductor $3366$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("c1")

sage: E.isogeny_class()

## Elliptic curves in class 3366.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3366.c1 3366i2 $$[1, -1, 0, -1638, -25110]$$ $$666940371553/37026$$ $$26991954$$ $$$$ $$1536$$ $$0.49129$$
3366.c2 3366i1 $$[1, -1, 0, -108, -324]$$ $$192100033/38148$$ $$27809892$$ $$$$ $$768$$ $$0.14472$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 3366.c have rank $$1$$.

## Complex multiplication

The elliptic curves in class 3366.c do not have complex multiplication.

## Modular form3366.2.a.c

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - 2q^{5} - 2q^{7} - q^{8} + 2q^{10} + q^{11} + 4q^{13} + 2q^{14} + q^{16} - q^{17} + 2q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 