Properties

Label 355740.bs
Number of curves $4$
Conductor $355740$
CM no
Rank $1$
Graph

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

Elliptic curves in class 355740.bs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
355740.bs1 355740bs4 \([0, -1, 0, -294056660, 1023422250600]\) \(52702650535889104/22020583921875\) \(1174933123058368904076000000\) \([2]\) \(179159040\) \(3.8913\)  
355740.bs2 355740bs2 \([0, -1, 0, -253502300, 1553618854152]\) \(33766427105425744/9823275\) \(524131931076805497600\) \([2]\) \(59719680\) \(3.3420\)  
355740.bs3 355740bs1 \([0, -1, 0, -15779045, 24487788690]\) \(-130287139815424/2250652635\) \(-7505382063044470152240\) \([2]\) \(29859840\) \(2.9954\) \(\Gamma_0(N)\)-optimal
355740.bs4 355740bs3 \([0, -1, 0, 61060795, 117304552422]\) \(7549996227362816/6152409907875\) \(-20516798660519243588814000\) \([2]\) \(89579520\) \(3.5448\)  

Rank

sage: E.rank()
 

The elliptic curves in class 355740.bs have rank \(1\).

Complex multiplication

The elliptic curves in class 355740.bs do not have complex multiplication.

Modular form 355740.2.a.bs

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + q^{9} + 2q^{13} - q^{15} - 6q^{17} + 8q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.