Properties

Label 193830.cc
Number of curves $2$
Conductor $193830$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("cc1")
 
E.isogeny_class()
 

Elliptic curves in class 193830.cc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
193830.cc1 193830f2 \([1, 0, 0, -97511805, -371006520105]\) \(-102540468901688739487767312721/119848113393926474790870\) \(-119848113393926474790870\) \([]\) \(45715040\) \(3.3406\)  
193830.cc2 193830f1 \([1, 0, 0, 120345, 195518025]\) \(192755882359997444879/16624047233430000000\) \(-16624047233430000000\) \([7]\) \(6530720\) \(2.3676\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 193830.cc have rank \(0\).

Complex multiplication

The elliptic curves in class 193830.cc do not have complex multiplication.

Modular form 193830.2.a.cc

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} + q^{7} + q^{8} + q^{9} + q^{10} + 5 q^{11} + q^{12} - q^{13} + q^{14} + q^{15} + q^{16} - 3 q^{17} + q^{18} + 6 q^{19} + O(q^{20})\) Copy content 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.