Properties

 Label 1008.a Number of curves 2 Conductor 1008 CM no Rank 0 Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("1008.a1")

sage: E.isogeny_class()

Elliptic curves in class 1008.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1008.a1 1008m2 [0, 0, 0, -327, -2270] [2] 384
1008.a2 1008m1 [0, 0, 0, -12, -65] [2] 192 $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 1008.a have rank $$0$$.

Modular form1008.2.a.a

sage: E.q_eigenform(10)

$$q - 4q^{5} + q^{7} + 2q^{11} - 6q^{13} + 4q^{17} + 4q^{19} + O(q^{20})$$

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.