Properties

Label 350658.ba
Number of curves $2$
Conductor $350658$
CM no
Rank $0$
Graph

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

Elliptic curves in class 350658.ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
350658.ba1 350658ba2 \([1, -1, 0, -659412, 193118800]\) \(24553362849625/1755162752\) \(2266736474589890688\) \([2]\) \(6881280\) \(2.2690\)  
350658.ba2 350658ba1 \([1, -1, 0, 37548, 13163728]\) \(4533086375/60669952\) \(-78353299688767488\) \([2]\) \(3440640\) \(1.9224\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 350658.ba have rank \(0\).

Complex multiplication

The elliptic curves in class 350658.ba do not have complex multiplication.

Modular form 350658.2.a.ba

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{7} - q^{8} + q^{14} + q^{16} + 6q^{17} + 6q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.