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Properties

Label 70805.ba
Number of curves $2$
Conductor $70805$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ba1")
 
E.isogeny_class()
 

Elliptic curves in class 70805.ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
70805.ba1 70805y2 \([0, -1, 1, -119877585, -296794916202]\) \(1369177719046144/518798828125\) \(72189965589876495361328125\) \([]\) \(16692480\) \(3.6612\)  
70805.ba2 70805y1 \([0, -1, 1, -52471225, 146295735781]\) \(114817869021184/15353125\) \(2136360965680569053125\) \([]\) \(5564160\) \(3.1119\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 70805.2.a.ba

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2 q^{4} + q^{5} - 2 q^{9} + 6 q^{11} + 2 q^{12} - 4 q^{13} - q^{15} + 4 q^{16} - 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.