Properties

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

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

Elliptic curves in class 97461l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
97461.s4 97461l1 [1, -1, 0, -725013, 237792456] [2] 589824 \(\Gamma_0(N)\)-optimal
97461.s3 97461l2 [1, -1, 0, -727218, 236274975] [2, 2] 1179648  
97461.s5 97461l3 [1, -1, 0, -125253, 615151746] [2] 2359296  
97461.s2 97461l4 [1, -1, 0, -1364463, -239747040] [2, 2] 2359296  
97461.s6 97461l5 [1, -1, 0, 4970502, -1839959199] [2] 4718592  
97461.s1 97461l6 [1, -1, 0, -17895348, -29112590781] [2] 4718592  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 97461.2.a.l

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.