Properties

 Label 85176.bo Number of curves $2$ Conductor $85176$ CM no Rank $0$ Graph

Related objects

Show commands: SageMath
sage: E = EllipticCurve("bo1")

sage: E.isogeny_class()

Elliptic curves in class 85176.bo

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
85176.bo1 85176bg1 $$[0, 0, 0, -9796254, -11801526035]$$ $$49860882714802176/57967$$ $$120871715314896$$ $$[2]$$ $$1290240$$ $$2.4165$$ $$\Gamma_0(N)$$-optimal
85176.bo2 85176bg2 $$[0, 0, 0, -9793719, -11807939078]$$ $$-3113886554501616/3360173089$$ $$-112105131546537222912$$ $$[2]$$ $$2580480$$ $$2.7631$$

Rank

sage: E.rank()

The elliptic curves in class 85176.bo have rank $$0$$.

Complex multiplication

The elliptic curves in class 85176.bo do not have complex multiplication.

Modular form 85176.2.a.bo

sage: E.q_eigenform(10)

$$q + 2q^{5} - q^{7} - 2q^{11} + 6q^{17} - 4q^{19} + O(q^{20})$$

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.