Properties

 Label 1002.d Number of curves 2 Conductor 1002 CM no Rank 1 Graph Related objects

Show commands for: SageMath
sage: E = EllipticCurve("1002.d1")
sage: E.isogeny_class()

Elliptic curves in class 1002.d

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
1002.d1 1002d2 [1, 0, 1, -125, -544] 2 288
1002.d2 1002d1 [1, 0, 1, -5, -16] 2 144 $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 1002.d have rank $$1$$.

Modular form1002.2.a.d

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

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 LMFDB numbering.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with LMFDB labels. 