Properties

Label 70805.bd
Number of curves $3$
Conductor $70805$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bd1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 70805.bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
70805.bd1 70805e3 \([0, 1, 1, -1859811, 1020602020]\) \(-250523582464/13671875\) \(-38824855443294921875\) \([]\) \(1451520\) \(2.5170\)  
70805.bd2 70805e1 \([0, 1, 1, -18881, -1114130]\) \(-262144/35\) \(-99391629934835\) \([]\) \(161280\) \(1.4184\) \(\Gamma_0(N)\)-optimal
70805.bd3 70805e2 \([0, 1, 1, 122729, 2865111]\) \(71991296/42875\) \(-121754746670172875\) \([]\) \(483840\) \(1.9677\)  

Rank

sage: E.rank()
 

The elliptic curves in class 70805.bd have rank \(0\).

Complex multiplication

The elliptic curves in class 70805.bd do not have complex multiplication.

Modular form 70805.2.a.bd

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2q^{4} - q^{5} - 2q^{9} + 3q^{11} - 2q^{12} - 5q^{13} - q^{15} + 4q^{16} - 2q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.