Properties

 Label 660.a Number of curves $2$ Conductor $660$ CM no Rank $0$ Graph Related objects

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

sage: E.isogeny_class()

Elliptic curves in class 660.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
660.a1 660a2 $$[0, -1, 0, -396, -2904]$$ $$26894628304/9075$$ $$2323200$$ $$$$ $$192$$ $$0.19367$$
660.a2 660a1 $$[0, -1, 0, -21, -54]$$ $$-67108864/61875$$ $$-990000$$ $$$$ $$96$$ $$-0.15290$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 660.a have rank $$0$$.

Complex multiplication

The elliptic curves in class 660.a do not have complex multiplication.

Modular form660.2.a.a

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} - 2 q^{7} + q^{9} - q^{11} + 2 q^{13} + q^{15} + 8 q^{17} - 2 q^{19} + O(q^{20})$$ 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. 