Properties

Label 97020.k
Number of curves $2$
Conductor $97020$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 97020.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
97020.k1 97020bm2 \([0, 0, 0, -33663, 2357782]\) \(192143824/1815\) \(39850370461440\) \([2]\) \(294912\) \(1.4304\)  
97020.k2 97020bm1 \([0, 0, 0, -588, 88837]\) \(-16384/2475\) \(-3396338391600\) \([2]\) \(147456\) \(1.0839\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 97020.k have rank \(0\).

Complex multiplication

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

Modular form 97020.2.a.k

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.