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Properties

Label 2310.u
Number of curves $8$
Conductor $2310$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 2310.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2310.u1 2310t7 \([1, 0, 0, -5324001, -4728746769]\) \(16689299266861680229173649/2396798250\) \(2396798250\) \([2]\) \(41472\) \(2.1224\)  
2310.u2 2310t8 \([1, 0, 0, -341501, -69817269]\) \(4404531606962679693649/444872222400201750\) \(444872222400201750\) \([2]\) \(41472\) \(2.1224\)  
2310.u3 2310t6 \([1, 0, 0, -332751, -73907019]\) \(4074571110566294433649/48828650062500\) \(48828650062500\) \([2, 2]\) \(20736\) \(1.7758\)  
2310.u4 2310t5 \([1, 0, 0, -75011, 7885545]\) \(46676570542430835889/106752955783320\) \(106752955783320\) \([6]\) \(13824\) \(1.5731\)  
2310.u5 2310t4 \([1, 0, 0, -65811, -6474375]\) \(31522423139920199089/164434491947880\) \(164434491947880\) \([6]\) \(13824\) \(1.5731\)  
2310.u6 2310t3 \([1, 0, 0, -20251, -1219519]\) \(-918468938249433649/109183593750000\) \(-109183593750000\) \([2]\) \(10368\) \(1.4293\)  
2310.u7 2310t2 \([1, 0, 0, -6411, 23985]\) \(29141055407581489/16604321025600\) \(16604321025600\) \([2, 6]\) \(6912\) \(1.2265\)  
2310.u8 2310t1 \([1, 0, 0, 1589, 3185]\) \(443688652450511/260789760000\) \(-260789760000\) \([6]\) \(3456\) \(0.87997\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2310.u have rank \(0\).

Complex multiplication

The elliptic curves in class 2310.u do not have complex multiplication.

Modular form 2310.2.a.u

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + q^{7} + q^{8} + q^{9} - q^{10} - q^{11} + q^{12} + 2 q^{13} + q^{14} - q^{15} + q^{16} + 6 q^{17} + q^{18} - 4 q^{19} + O(q^{20})\) 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 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.