# Properties

 Label 306c Number of curves 6 Conductor 306 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("306.b1")

sage: E.isogeny_class()

## Elliptic curves in class 306c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
306.b5 306c1 [1, -1, 0, -306, -1836] [2] 128 $$\Gamma_0(N)$$-optimal
306.b4 306c2 [1, -1, 0, -1026, 10692] [2, 2] 256
306.b2 306c3 [1, -1, 0, -15606, 754272] [2, 2] 512
306.b6 306c4 [1, -1, 0, 2034, 60264] [2] 512
306.b1 306c5 [1, -1, 0, -249696, 48087270] [2] 1024
306.b3 306c6 [1, -1, 0, -14796, 835434] [2] 1024

## Rank

sage: E.rank()

The elliptic curves in class 306c have rank $$0$$.

## Modular form306.2.a.b

sage: E.q_eigenform(10)

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

## 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 Cremona numbering.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.