Properties

Label 26520.s
Number of curves $4$
Conductor $26520$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 26520.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
26520.s1 26520e4 \([0, 1, 0, -2348856, -92595600]\) \(699782572199712476018/403188655517578125\) \(825730366500000000000\) \([2]\) \(1327104\) \(2.7031\)  
26520.s2 26520e2 \([0, 1, 0, -1557936, 745146864]\) \(408387906477526456516/1765480810640625\) \(1807852350096000000\) \([2, 2]\) \(663552\) \(2.3566\)  
26520.s3 26520e1 \([0, 1, 0, -1556316, 746781120]\) \(1628461040201585189584/30630848625\) \(7841497248000\) \([2]\) \(331776\) \(2.0100\) \(\Gamma_0(N)\)-optimal
26520.s4 26520e3 \([0, 1, 0, -792936, 1478322864]\) \(-26922086450129858258/445575877967449125\) \(-912539398077335808000\) \([2]\) \(1327104\) \(2.7031\)  

Rank

sage: E.rank()
 

The elliptic curves in class 26520.s have rank \(1\).

Complex multiplication

The elliptic curves in class 26520.s do not have complex multiplication.

Modular form 26520.2.a.s

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} - 4 q^{7} + q^{9} + 4 q^{11} - q^{13} - q^{15} + q^{17} - 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.