Properties

Label 38962f
Number of curves $4$
Conductor $38962$
CM no
Rank $0$
Graph

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

Elliptic curves in class 38962f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
38962.c3 38962f1 \([1, 0, 1, -3695101, -2997790248]\) \(-3149534523783390625/368345236897792\) \(-652546056223889293312\) \([2]\) \(1658880\) \(2.7300\) \(\Gamma_0(N)\)-optimal
38962.c2 38962f2 \([1, 0, 1, -60690941, -181987526184]\) \(13955300880533969118625/162273186639872\) \(287476848796918280192\) \([2]\) \(3317760\) \(3.0766\)  
38962.c4 38962f3 \([1, 0, 1, 23408899, 5184148440]\) \(800775157152056609375/469960256734490368\) \(-832563262380810490824448\) \([2]\) \(4976640\) \(3.2793\)  
38962.c1 38962f4 \([1, 0, 1, -94367661, 41600660792]\) \(52461072723569038782625/29937242318698495088\) \(53035650939355824656592368\) \([2]\) \(9953280\) \(3.6259\)  

Rank

sage: E.rank()
 

The elliptic curves in class 38962f have rank \(0\).

Complex multiplication

The elliptic curves in class 38962f do not have complex multiplication.

Modular form 38962.2.a.f

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.