# Properties

 Label 3234.m Number of curves $2$ Conductor $3234$ CM no Rank $0$ Graph # Related objects

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

E.isogeny_class()

## Elliptic curves in class 3234.m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3234.m1 3234m2 $$[1, 0, 1, -3541011, -2565008834]$$ $$121681065322255375/12702096$$ $$512575390060272$$ $$$$ $$57344$$ $$2.2515$$
3234.m2 3234m1 $$[1, 0, 1, -220771, -40298338]$$ $$-29489309167375/303595776$$ $$-12251184631564032$$ $$$$ $$28672$$ $$1.9049$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 3234.m have rank $$0$$.

## Complex multiplication

The elliptic curves in class 3234.m do not have complex multiplication.

## Modular form3234.2.a.m

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} - q^{6} - q^{8} + q^{9} + q^{11} + q^{12} + 4 q^{13} + q^{16} - 4 q^{17} - q^{18} + O(q^{20})$$

## 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. 