Properties

Label 148225.ba
Number of curves $2$
Conductor $148225$
CM no
Rank $0$
Graph

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

Elliptic curves in class 148225.ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
148225.ba1 148225y2 \([1, 0, 0, -629451138, 6078373746017]\) \(-162677523113838677\) \(-169543923828125\) \([]\) \(12787200\) \(3.2742\)  
148225.ba2 148225y1 \([1, 0, 0, -24263, -1585858]\) \(-9317\) \(-169543923828125\) \([]\) \(345600\) \(1.4687\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 148225.ba have rank \(0\).

Complex multiplication

The elliptic curves in class 148225.ba do not have complex multiplication.

Modular form 148225.2.a.ba

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} - q^{4} - q^{6} + 3 q^{8} - 2 q^{9} - q^{12} + 2 q^{13} - q^{16} + 2 q^{17} + 2 q^{18} + 6 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 37 \\ 37 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.