Properties

 Label 660.b Number of curves $2$ Conductor $660$ CM no Rank $1$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("b1")

sage: E.isogeny_class()

Elliptic curves in class 660.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
660.b1 660b2 $$[0, -1, 0, -76, 280]$$ $$192143824/1815$$ $$464640$$ $$$$ $$96$$ $$-0.091829$$
660.b2 660b1 $$[0, -1, 0, -1, 10]$$ $$-16384/2475$$ $$-39600$$ $$$$ $$48$$ $$-0.43840$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 660.b have rank $$1$$.

Complex multiplication

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

Modular form660.2.a.b

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} + q^{9} + q^{11} - 4 q^{13} + q^{15} - 2 q^{17} + 2 q^{19} + O(q^{20})$$ 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. 