Properties

Label 97461.s
Number of curves $6$
Conductor $97461$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more about

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

Elliptic curves in class 97461.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
97461.s1 97461l6 \([1, -1, 0, -17895348, -29112590781]\) \(7389727131216686257/6115533215337\) \(524505561726112197777\) \([2]\) \(4718592\) \(2.9041\)  
97461.s2 97461l4 \([1, -1, 0, -1364463, -239747040]\) \(3275619238041697/1605271262049\) \(137677889298717241929\) \([2, 2]\) \(2359296\) \(2.5576\)  
97461.s3 97461l2 \([1, -1, 0, -727218, 236274975]\) \(495909170514577/6224736609\) \(533871513200623689\) \([2, 2]\) \(1179648\) \(2.2110\)  
97461.s4 97461l1 \([1, -1, 0, -725013, 237792456]\) \(491411892194497/78897\) \(6766689648537\) \([2]\) \(589824\) \(1.8644\) \(\Gamma_0(N)\)-optimal
97461.s5 97461l3 \([1, -1, 0, -125253, 615151746]\) \(-2533811507137/1904381781393\) \(-163331438293147586553\) \([2]\) \(2359296\) \(2.5576\)  
97461.s6 97461l5 \([1, -1, 0, 4970502, -1839959199]\) \(158346567380527343/108665074944153\) \(-9319781966134294440513\) \([2]\) \(4718592\) \(2.9041\)  

Rank

sage: E.rank()
 

The elliptic curves in class 97461.s have rank \(0\).

Complex multiplication

The elliptic curves in class 97461.s do not have complex multiplication.

Modular form 97461.2.a.s

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} - 2q^{5} - 3q^{8} - 2q^{10} + 4q^{11} - q^{13} - q^{16} + q^{17} + 4q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 8 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.