Properties

 Label 13552.w Number of curves 6 Conductor 13552 CM no Rank 0 Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("13552.w1")

sage: E.isogeny_class()

Elliptic curves in class 13552.w

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
13552.w1 13552ba6 [0, -1, 0, -5286288, -4676390464] [2] 207360
13552.w2 13552ba5 [0, -1, 0, -330128, -73109056] [2] 103680
13552.w3 13552ba4 [0, -1, 0, -68768, -5666560] [2] 69120
13552.w4 13552ba2 [0, -1, 0, -20368, 1124928] [2] 23040
13552.w5 13552ba1 [0, -1, 0, -1008, 25280] [2] 11520 $$\Gamma_0(N)$$-optimal
13552.w6 13552ba3 [0, -1, 0, 8672, -524544] [2] 34560

Rank

sage: E.rank()

The elliptic curves in class 13552.w have rank $$0$$.

Modular form 13552.2.a.w

sage: E.q_eigenform(10)

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

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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 9 & 18 & 6 \\ 2 & 1 & 6 & 18 & 9 & 3 \\ 3 & 6 & 1 & 3 & 6 & 2 \\ 9 & 18 & 3 & 1 & 2 & 6 \\ 18 & 9 & 6 & 2 & 1 & 3 \\ 6 & 3 & 2 & 6 & 3 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with LMFDB labels.