Properties

 Label 111090.bs Number of curves $2$ Conductor $111090$ CM no Rank $1$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("bs1")

sage: E.isogeny_class()

Elliptic curves in class 111090.bs

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
111090.bs1 111090bs1 $$[1, 1, 1, -129616, -17200591]$$ $$1626794704081/83462400$$ $$12355430582073600$$ $$$$ $$1622016$$ $$1.8456$$ $$\Gamma_0(N)$$-optimal
111090.bs2 111090bs2 $$[1, 1, 1, 81984, -67646031]$$ $$411664745519/13605414480$$ $$-2014089627760272720$$ $$$$ $$3244032$$ $$2.1922$$

Rank

sage: E.rank()

The elliptic curves in class 111090.bs have rank $$1$$.

Complex multiplication

The elliptic curves in class 111090.bs do not have complex multiplication.

Modular form 111090.2.a.bs

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} + q^{4} - q^{5} - q^{6} - q^{7} + q^{8} + q^{9} - q^{10} + 6 q^{11} - q^{12} - q^{14} + q^{15} + q^{16} - 6 q^{17} + q^{18} + 8 q^{19} + O(q^{20})$$ 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. 