# Properties

 Label 3330.m Number of curves $4$ Conductor $3330$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("m1")

sage: E.isogeny_class()

## Elliptic curves in class 3330.m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3330.m1 3330s4 $$[1, -1, 1, -94388, 5005847]$$ $$127568139540190201/59114336463360$$ $$43094351281789440$$ $$[6]$$ $$48384$$ $$1.8864$$
3330.m2 3330s2 $$[1, -1, 1, -47813, -4011883]$$ $$16581570075765001/998001000$$ $$727542729000$$ $$[2]$$ $$16128$$ $$1.3371$$
3330.m3 3330s1 $$[1, -1, 1, -2813, -69883]$$ $$-3375675045001/999000000$$ $$-728271000000$$ $$[2]$$ $$8064$$ $$0.99057$$ $$\Gamma_0(N)$$-optimal
3330.m4 3330s3 $$[1, -1, 1, 20812, 582167]$$ $$1367594037332999/995878502400$$ $$-725995428249600$$ $$[6]$$ $$24192$$ $$1.5399$$

## Rank

sage: E.rank()

The elliptic curves in class 3330.m have rank $$0$$.

## Complex multiplication

The elliptic curves in class 3330.m do not have complex multiplication.

## Modular form3330.2.a.m

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} - q^{5} - 4q^{7} + q^{8} - q^{10} - 6q^{11} + 2q^{13} - 4q^{14} + q^{16} + 6q^{17} + 2q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.