# Properties

 Label 3234.d Number of curves 4 Conductor 3234 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("3234.d1")

sage: E.isogeny_class()

## Elliptic curves in class 3234.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3234.d1 3234b3 [1, 1, 0, -3945, 93381]  4320
3234.d2 3234b4 [1, 1, 0, -1985, 188637]  8640
3234.d3 3234b1 [1, 1, 0, -270, -1728]  1440 $$\Gamma_0(N)$$-optimal
3234.d4 3234b2 [1, 1, 0, 220, -6726]  2880

## Rank

sage: E.rank()

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

## Modular form3234.2.a.d

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} + q^{6} - q^{8} + q^{9} - q^{11} - q^{12} + 4q^{13} + q^{16} + 6q^{17} - q^{18} + 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 