Properties

Label 35520s
Number of curves $4$
Conductor $35520$
CM no
Rank $1$
Graph

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

Elliptic curves in class 35520s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
35520.bl3 35520s1 \([0, -1, 0, -12488865, 16991784225]\) \(821774646379511057449/38361600000\) \(10056263270400000\) \([2]\) \(1105920\) \(2.5494\) \(\Gamma_0(N)\)-optimal
35520.bl2 35520s2 \([0, -1, 0, -12509345, 16933281057]\) \(825824067562227826729/5613755625000000\) \(1471612354560000000000\) \([2, 2]\) \(2211840\) \(2.8959\)  
35520.bl4 35520s3 \([0, -1, 0, -4837025, 37475150625]\) \(-47744008200656797609/2286529541015625000\) \(-599400000000000000000000\) \([4]\) \(4423680\) \(3.2425\)  
35520.bl1 35520s4 \([0, -1, 0, -20509345, -7353118943]\) \(3639478711331685826729/2016912141902025000\) \(528721416526764441600000\) \([2]\) \(4423680\) \(3.2425\)  

Rank

sage: E.rank()
 

The elliptic curves in class 35520s have rank \(1\).

Complex multiplication

The elliptic curves in class 35520s do not have complex multiplication.

Modular form 35520.2.a.s

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + 4 q^{7} + q^{9} - 4 q^{11} - 2 q^{13} - q^{15} - 2 q^{17} + O(q^{20})\) 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 Cremona 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 Cremona labels.