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Properties

Label 33930f
Number of curves $2$
Conductor $33930$
CM no
Rank $0$
Graph

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

Elliptic curves in class 33930f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
33930.k2 33930f1 \([1, -1, 0, 24855771, -41346788715]\) \(62898697943298124177490037/63744399417968386000000\) \(-1721098784285146422000000\) \([3]\) \(4717440\) \(3.3373\) \(\Gamma_0(N)\)-optimal
33930.k1 33930f2 \([1, -1, 0, -606209604, -5798268414640]\) \(-1251701744499641551742491347/13559824919198275993600\) \(-266898033884579666382028800\) \([]\) \(14152320\) \(3.8866\)  

Rank

sage: E.rank()
 

The elliptic curves in class 33930f have rank \(0\).

Complex multiplication

The elliptic curves in class 33930f do not have complex multiplication.

Modular form 33930.2.a.f

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{5} + 2 q^{7} - q^{8} - q^{10} - 3 q^{11} + q^{13} - 2 q^{14} + q^{16} + 3 q^{17} - 4 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.