Properties

Label 5850.t
Number of curves $2$
Conductor $5850$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("t1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5850.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5850.t1 5850u2 \([1, -1, 0, -36117, 458541]\) \(3659383421/2056392\) \(2927948765625000\) \([2]\) \(30720\) \(1.6579\)  
5850.t2 5850u1 \([1, -1, 0, 8883, 53541]\) \(54439939/32448\) \(-46200375000000\) \([2]\) \(15360\) \(1.3113\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 5850.t have rank \(1\).

Complex multiplication

The elliptic curves in class 5850.t do not have complex multiplication.

Modular form 5850.2.a.t

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