Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 97020.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
97020.c1 97020bn2 \([0, 0, 0, -337008, -75302332]\) \(462893166690304/4125\) \(37721376000\) \([]\) \(373248\) \(1.6126\)  
97020.c2 97020bn1 \([0, 0, 0, -4368, -92428]\) \(1007878144/179685\) \(1643143138560\) \([]\) \(124416\) \(1.0633\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 97020.2.a.c

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.