Properties

 Label 90.a Number of curves 4 Conductor 90 CM no Rank 0 Graph Related objects

Show commands for: SageMath
sage: E = EllipticCurve("90.a1")
sage: E.isogeny_class()

Elliptic curves in class 90.a

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
90.a1 90a4 [1, -1, 0, -1149, -14707] 2 48
90.a2 90a3 [1, -1, 0, -69, -235] 2 24
90.a3 90a2 [1, -1, 0, -24, 18] 6 16
90.a4 90a1 [1, -1, 0, 6, 0] 6 8 $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 90.a have rank $$0$$.

Modular form90.2.a.a

sage: E.q_eigenform(10)
$$q - q^{2} + q^{4} + q^{5} + 2q^{7} - q^{8} - q^{10} + 6q^{11} - 4q^{13} - 2q^{14} + q^{16} - 6q^{17} - 4q^{19} + O(q^{20})$$

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels. 