# Properties

 Label 327990.m Number of curves $2$ Conductor $327990$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 327990.m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
327990.m1 327990m2 $$[1, 0, 1, -38704, -2628628]$$ $$10779215329/1232010$$ $$732828279705210$$ $$$$ $$2376192$$ $$1.5846$$
327990.m2 327990m1 $$[1, 0, 1, 3346, -206548]$$ $$6967871/35100$$ $$-20878298567100$$ $$$$ $$1188096$$ $$1.2380$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 327990.m have rank $$0$$.

## Complex multiplication

The elliptic curves in class 327990.m do not have complex multiplication.

## Modular form 327990.2.a.m

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} + 2q^{7} - q^{8} + q^{9} + q^{10} - 4q^{11} + q^{12} - q^{13} - 2q^{14} - q^{15} + q^{16} - 8q^{17} - q^{18} + 6q^{19} + O(q^{20})$$ ## 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. 