↑

Properties

Label 302330.bo
Number of curves $2$
Conductor $302330$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("bo1")
 
E.isogeny_class()
 

Elliptic curves in class 302330.bo

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
302330.bo1 302330bo2 \([1, -1, 1, -62268303, 827481250957]\) \(-226953328047600468451761/2382836194386693393110\) \(-280338295433400091005998390\) \([]\) \(293190912\) \(3.7570\)  
302330.bo2 302330bo1 \([1, -1, 1, -6753753, -6855595463]\) \(-289581579184798874961/5081260310000000\) \(-597805194211190000000\) \([]\) \(41884416\) \(2.7840\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 302330.bo have rank \(0\).

Complex multiplication

The elliptic curves in class 302330.bo do not have complex multiplication.

Modular form 302330.2.a.bo

sage: E.q_eigenform(10)
 
\(q + q^{2} + 3 q^{3} + q^{4} - q^{5} + 3 q^{6} + q^{8} + 6 q^{9} - q^{10} - 2 q^{11} + 3 q^{12} + 7 q^{13} - 3 q^{15} + q^{16} - 4 q^{17} + 6 q^{18} + q^{19} + O(q^{20})\) Copy content Toggle raw display

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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.