Properties

Label 97020.f
Number of curves $4$
Conductor $97020$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 97020.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
97020.f1 97020bk4 \([0, 0, 0, -110248383, -445560267418]\) \(6749703004355978704/5671875\) \(124532407692000000\) \([2]\) \(4976640\) \(3.0158\)  
97020.f2 97020bk3 \([0, 0, 0, -6889008, -6965095543]\) \(-26348629355659264/24169921875\) \(-33167367105468750000\) \([2]\) \(2488320\) \(2.6692\)  
97020.f3 97020bk2 \([0, 0, 0, -1391943, -582034642]\) \(13584145739344/1195803675\) \(26255217326667436800\) \([2]\) \(1658880\) \(2.4665\)  
97020.f4 97020bk1 \([0, 0, 0, 96432, -42349867]\) \(72268906496/606436875\) \(-832187814401790000\) \([2]\) \(829440\) \(2.1199\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 97020.2.a.f

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.