Properties

 Label 11109i Number of curves 6 Conductor 11109 CM no Rank 0 Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("11109.d1")

sage: E.isogeny_class()

Elliptic curves in class 11109i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
11109.d6 11109i1 [1, 0, 0, 518, 1043] [2] 6336 $$\Gamma_0(N)$$-optimal
11109.d5 11109i2 [1, 0, 0, -2127, 7920] [2, 2] 12672
11109.d3 11109i3 [1, 0, 0, -20642, -1136307] [2] 25344
11109.d2 11109i4 [1, 0, 0, -25932, 1602855] [2, 2] 25344
11109.d1 11109i5 [1, 0, 0, -414747, 102772518] [2] 50688
11109.d4 11109i6 [1, 0, 0, -17997, 2604252] [2] 50688

Rank

sage: E.rank()

The elliptic curves in class 11109i have rank $$0$$.

Modular form 11109.2.a.d

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} - q^{4} + 2q^{5} - q^{6} + q^{7} + 3q^{8} + q^{9} - 2q^{10} - 4q^{11} - q^{12} - 2q^{13} - q^{14} + 2q^{15} - q^{16} + 6q^{17} - q^{18} - 4q^{19} + O(q^{20})$$

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.