Properties

 Label 87360.bl Number of curves 8 Conductor 87360 CM no Rank 0 Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("87360.bl1")

sage: E.isogeny_class()

Elliptic curves in class 87360.bl

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
87360.bl1 87360m8 [0, -1, 0, -2572189121, -50210557479999] [2] 21233664
87360.bl2 87360m6 [0, -1, 0, -160761921, -784498732479] [2, 2] 10616832
87360.bl3 87360m7 [0, -1, 0, -158786241, -804722188095] [2] 21233664
87360.bl4 87360m5 [0, -1, 0, -31769921, -68800473279] [2] 7077888
87360.bl5 87360m3 [0, -1, 0, -10171201, -11938220735] [2] 5308416
87360.bl6 87360m2 [0, -1, 0, -2649921, -292761279] [2, 2] 3538944
87360.bl7 87360m1 [0, -1, 0, -1646401, 809304385] [2] 1769472 $$\Gamma_0(N)$$-optimal
87360.bl8 87360m4 [0, -1, 0, 10413759, -2333308095] [2] 7077888

Rank

sage: E.rank()

The elliptic curves in class 87360.bl have rank $$0$$.

Modular form 87360.2.a.bl

sage: E.q_eigenform(10)

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

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.

$$\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 3 & 4 & 6 & 12 & 12 \\ 2 & 1 & 2 & 6 & 2 & 3 & 6 & 6 \\ 4 & 2 & 1 & 12 & 4 & 6 & 12 & 3 \\ 3 & 6 & 12 & 1 & 12 & 2 & 4 & 4 \\ 4 & 2 & 4 & 12 & 1 & 6 & 3 & 12 \\ 6 & 3 & 6 & 2 & 6 & 1 & 2 & 2 \\ 12 & 6 & 12 & 4 & 3 & 2 & 1 & 4 \\ 12 & 6 & 3 & 4 & 12 & 2 & 4 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with LMFDB labels.