Properties

 Label 336.a Number of curves 6 Conductor 336 CM no Rank 1 Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("336.a1")

sage: E.isogeny_class()

Elliptic curves in class 336.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
336.a1 336e5 [0, -1, 0, -12544, 544960] [4] 256
336.a2 336e4 [0, -1, 0, -784, 8704] [2, 4] 128
336.a3 336e3 [0, -1, 0, -624, -5760] [2] 128
336.a4 336e6 [0, -1, 0, -544, 13888] [4] 256
336.a5 336e2 [0, -1, 0, -64, 64] [2, 2] 64
336.a6 336e1 [0, -1, 0, 16, 0] [2] 32 $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 336.a have rank $$1$$.

Modular form336.2.a.a

sage: E.q_eigenform(10)

$$q - q^{3} - 2q^{5} + q^{7} + q^{9} - 4q^{11} - 2q^{13} + 2q^{15} - 6q^{17} - 4q^{19} + O(q^{20})$$

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.