Properties

Label 2850.ba
Number of curves $2$
Conductor $2850$
CM no
Rank $0$
Graph

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

Elliptic curves in class 2850.ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2850.ba1 2850y2 \([1, 0, 0, -9938, 379992]\) \(6947097508441/10687500\) \(166992187500\) \([2]\) \(4608\) \(1.0528\)  
2850.ba2 2850y1 \([1, 0, 0, -438, 9492]\) \(-594823321/2166000\) \(-33843750000\) \([2]\) \(2304\) \(0.70621\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2850.ba have rank \(0\).

Complex multiplication

The elliptic curves in class 2850.ba do not have complex multiplication.

Modular form 2850.2.a.ba

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} + 2 q^{7} + q^{8} + q^{9} - 2 q^{11} + q^{12} + 2 q^{14} + q^{16} + 2 q^{17} + q^{18} + q^{19} + O(q^{20})\)  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.