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Properties

Label 3850.bb
Number of curves $2$
Conductor $3850$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bb1")
 
E.isogeny_class()
 

Elliptic curves in class 3850.bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3850.bb1 3850u2 \([1, 1, 1, -21188, 1125781]\) \(67324767141241/3368750000\) \(52636718750000\) \([2]\) \(12288\) \(1.3916\)  
3850.bb2 3850u1 \([1, 1, 1, 812, 69781]\) \(3789119879/135520000\) \(-2117500000000\) \([2]\) \(6144\) \(1.0450\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 3850.bb have rank \(0\).

Complex multiplication

The elliptic curves in class 3850.bb do not have complex multiplication.

Modular form 3850.2.a.bb

sage: E.q_eigenform(10)
 
\(q + q^{2} + 2 q^{3} + q^{4} + 2 q^{6} + q^{7} + q^{8} + q^{9} + q^{11} + 2 q^{12} + q^{14} + q^{16} + q^{18} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.