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Properties

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

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Show commands: SageMath
E = EllipticCurve("z1")
 
E.isogeny_class()
 

Elliptic curves in class 3850.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3850.z1 3850y1 \([1, 0, 0, -12893013, 17818146017]\) \(-606773969327363726065/14480963796992\) \(-5656626483200000000\) \([3]\) \(194400\) \(2.7094\) \(\Gamma_0(N)\)-optimal
3850.z2 3850y2 \([1, 0, 0, -4213013, 41270106017]\) \(-21171034581520602865/1871407179898211648\) \(-731018429647738925000000\) \([]\) \(583200\) \(3.2587\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 3850.2.a.z

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} + q^{7} + q^{8} - 2 q^{9} - q^{11} + q^{12} + 2 q^{13} + q^{14} + q^{16} + 3 q^{17} - 2 q^{18} + 8 q^{19} + O(q^{20})\) 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.