Properties

Label 97020.d
Number of curves $4$
Conductor $97020$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 97020.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
97020.d1 97020f3 \([0, 0, 0, -2931768, 1932150213]\) \(75216478666752/326095\) \(12082134194277840\) \([2]\) \(1492992\) \(2.2927\)  
97020.d2 97020f4 \([0, 0, 0, -2885463, 1996134462]\) \(-4481782160112/310023175\) \(-183786521286672057600\) \([2]\) \(2985984\) \(2.6393\)  
97020.d3 97020f1 \([0, 0, 0, -50568, 353633]\) \(281370820608/161767375\) \(8221724597394000\) \([2]\) \(497664\) \(1.7434\) \(\Gamma_0(N)\)-optimal
97020.d4 97020f2 \([0, 0, 0, 201537, 2824262]\) \(1113258734352/648484375\) \(-527340936276000000\) \([2]\) \(995328\) \(2.0900\)  

Rank

sage: E.rank()
 

The elliptic curves in class 97020.d have rank \(1\).

Complex multiplication

The elliptic curves in class 97020.d do not have complex multiplication.

Modular form 97020.2.a.d

sage: E.q_eigenform(10)
 
\(q - q^{5} - q^{11} - 2q^{13} - 6q^{17} + 4q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.