Properties

 Label 99.d Number of curves 3 Conductor 99 CM no Rank 0 Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("99.d1")
sage: E.isogeny_class()

Elliptic curves in class 99.d

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
99.d1 99d3 [0, 0, 1, -70383, 7187035] 1 150
99.d2 99d2 [0, 0, 1, -93, 625] 1 30
99.d3 99d1 [0, 0, 1, -3, -5] 1 6 $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 99.d have rank $$0$$.

Modular form99.2.a.d

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

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.

$$\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with LMFDB labels.