Properties

Label 381150kb
Number of curves $4$
Conductor $381150$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("kb1")
 
E.isogeny_class()
 

Elliptic curves in class 381150kb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
381150.kb4 381150kb1 \([1, -1, 1, 6982645, 9453621147]\) \(1865864036231/2993760000\) \(-60411642919897500000000\) \([2]\) \(29491200\) \(3.0565\) \(\Gamma_0(N)\)-optimal
381150.kb3 381150kb2 \([1, -1, 1, -47467355, 96464721147]\) \(586145095611769/140040608400\) \(2825905626685505306250000\) \([2, 2]\) \(58982400\) \(3.4030\)  
381150.kb1 381150kb3 \([1, -1, 1, -709034855, 7266533286147]\) \(1953542217204454969/170843779260\) \(3447488572143695670937500\) \([2]\) \(117964800\) \(3.7496\)  
381150.kb2 381150kb4 \([1, -1, 1, -257099855, -1505546843853]\) \(93137706732176569/5369647977540\) \(108355130746852209629062500\) \([2]\) \(117964800\) \(3.7496\)  

Rank

sage: E.rank()
 

The elliptic curves in class 381150kb have rank \(0\).

Complex multiplication

The elliptic curves in class 381150kb do not have complex multiplication.

Modular form 381150.2.a.kb

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

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.