Properties

 Label 1480.b Number of curves $2$ Conductor $1480$ CM no Rank $1$ Graph

Related objects

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

E.isogeny_class()

Elliptic curves in class 1480.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1480.b1 1480c1 $$[0, 1, 0, -60, 160]$$ $$94875856/185$$ $$47360$$ $$[2]$$ $$192$$ $$-0.21435$$ $$\Gamma_0(N)$$-optimal
1480.b2 1480c2 $$[0, 1, 0, -40, 288]$$ $$-7086244/34225$$ $$-35046400$$ $$[2]$$ $$384$$ $$0.13222$$

Rank

sage: E.rank()

The elliptic curves in class 1480.b have rank $$1$$.

Complex multiplication

The elliptic curves in class 1480.b do not have complex multiplication.

Modular form1480.2.a.b

sage: E.q_eigenform(10)

$$q - 2 q^{3} + q^{5} + 2 q^{7} + q^{9} - 6 q^{13} - 2 q^{15} - 2 q^{17} + 6 q^{19} + O(q^{20})$$

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.