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Properties

Label 42350.cc
Number of curves $2$
Conductor $42350$
CM no
Rank $0$
Graph

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

Elliptic curves in class 42350.cc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
42350.cc1 42350cl1 \([1, 1, 1, -1288713, -564797969]\) \(-584043889/1400\) \(-567381163146875000\) \([]\) \(912384\) \(2.2860\) \(\Gamma_0(N)\)-optimal
42350.cc2 42350cl2 \([1, 1, 1, 2371537, -2841473469]\) \(3639707951/10718750\) \(-4344012030343261718750\) \([]\) \(2737152\) \(2.8353\)  

Rank

sage: E.rank()
 

The elliptic curves in class 42350.cc have rank \(0\).

Complex multiplication

The elliptic curves in class 42350.cc do not have complex multiplication.

Modular form 42350.2.a.cc

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.