Properties

Label 381150.gp
Number of curves $8$
Conductor $381150$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("gp1")
 
E.isogeny_class()
 

Elliptic curves in class 381150.gp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
381150.gp1 381150gp8 \([1, -1, 0, -144945927792, -21240092336707634]\) \(16689299266861680229173649/2396798250\) \(48365440125472722656250\) \([2]\) \(955514880\) \(4.6754\)  
381150.gp2 381150gp7 \([1, -1, 0, -9297365292, -313497736395134]\) \(4404531606962679693649/444872222400201750\) \(8977159773870388425980402343750\) \([2]\) \(955514880\) \(4.6754\)  
381150.gp3 381150gp6 \([1, -1, 0, -9059146542, -331872739676384]\) \(4074571110566294433649/48828650062500\) \(985322461331696844726562500\) \([2, 2]\) \(477757440\) \(4.3288\)  
381150.gp4 381150gp4 \([1, -1, 0, -2042175042, 35451444281116]\) \(46676570542430835889/106752955783320\) \(2154187859222360694954375000\) \([2]\) \(318504960\) \(4.1261\)  
381150.gp5 381150gp5 \([1, -1, 0, -1791705042, -29058617928884]\) \(31522423139920199089/164434491947880\) \(3318154364835553710245625000\) \([2]\) \(318504960\) \(4.1261\)  
381150.gp6 381150gp3 \([1, -1, 0, -551334042, -5470513113884]\) \(-918468938249433649/109183593750000\) \(-2203236157319274902343750000\) \([2]\) \(238878720\) \(3.9822\)  
381150.gp7 381150gp2 \([1, -1, 0, -174540042, 110187176116]\) \(29141055407581489/16604321025600\) \(335061699243056703225000000\) \([2, 2]\) \(159252480\) \(3.7795\)  
381150.gp8 381150gp1 \([1, -1, 0, 43259958, 13701776116]\) \(443688652450511/260789760000\) \(-5262525338799960000000000\) \([2]\) \(79626240\) \(3.4329\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 381150.2.a.gp

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{7} - q^{8} + 2 q^{13} - q^{14} + q^{16} - 6 q^{17} + 4 q^{19} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rrrrrrrr} 1 & 4 & 2 & 12 & 3 & 4 & 6 & 12 \\ 4 & 1 & 2 & 3 & 12 & 4 & 6 & 12 \\ 2 & 2 & 1 & 6 & 6 & 2 & 3 & 6 \\ 12 & 3 & 6 & 1 & 4 & 12 & 2 & 4 \\ 3 & 12 & 6 & 4 & 1 & 12 & 2 & 4 \\ 4 & 4 & 2 & 12 & 12 & 1 & 6 & 3 \\ 6 & 6 & 3 & 2 & 2 & 6 & 1 & 2 \\ 12 & 12 & 6 & 4 & 4 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.