Properties

 Label 1002.a Number of curves $2$ Conductor $1002$ CM no Rank $0$ Graph Related objects

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

sage: E.isogeny_class()

Elliptic curves in class 1002.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1002.a1 1002a2 $$[1, 1, 0, -860, -10074]$$ $$70470585447625/4518018$$ $$4518018$$ $$$$ $$384$$ $$0.33467$$
1002.a2 1002a1 $$[1, 1, 0, -50, -192]$$ $$-14260515625/4382748$$ $$-4382748$$ $$$$ $$192$$ $$-0.011904$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 1002.a have rank $$0$$.

Complex multiplication

The elliptic curves in class 1002.a do not have complex multiplication.

Modular form1002.2.a.a

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} + q^{6} - q^{8} + q^{9} - q^{12} - 4 q^{13} + q^{16} + 6 q^{17} - q^{18} + O(q^{20})$$ 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. 