# Properties

 Label 306.a Number of curves 4 Conductor 306 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("306.a1")

sage: E.isogeny_class()

## Elliptic curves in class 306.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
306.a1 306b4 [1, -1, 0, -1017, 8883]  288
306.a2 306b3 [1, -1, 0, -927, 11097]  144
306.a3 306b2 [1, -1, 0, -387, -2835]  96
306.a4 306b1 [1, -1, 0, -27, -27]  48 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 306.a have rank $$1$$.

## Modular form306.2.a.a

sage: E.q_eigenform(10)

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

## 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. 