↑

Properties

Label 102550.l
Number of curves $2$
Conductor $102550$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 102550.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
102550.l1 102550p2 \([1, -1, 0, -191177, 32221581]\) \(6181898977960775901/615365632\) \(76920704000\) \([2]\) \(394240\) \(1.5207\)  
102550.l2 102550p1 \([1, -1, 0, -11977, 503181]\) \(1520121299538141/15054405632\) \(1881800704000\) \([2]\) \(197120\) \(1.1741\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 102550.l have rank \(0\).

Complex multiplication

The elliptic curves in class 102550.l do not have complex multiplication.

Modular form 102550.2.a.l

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.