Properties

 Label 88270u Number of curves 2 Conductor 88270 CM no Rank 0 Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("88270.k1")

sage: E.isogeny_class()

Elliptic curves in class 88270u

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
88270.k2 88270u1 [1, -1, 1, 2810783433, 57129831452559] [7] 285815040 $$\Gamma_0(N)$$-optimal
88270.k1 88270u2 [1, -1, 1, -938726820567, -350077314766040241] [] 2000705280

Rank

sage: E.rank()

The elliptic curves in class 88270u have rank $$0$$.

Modular form 88270.2.a.k

sage: E.q_eigenform(10)

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

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.

$$\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with Cremona labels.