Properties

Label 52094.g
Number of curves $6$
Conductor $52094$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 52094.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
52094.g1 52094j6 \([1, 0, 0, -10160268, -12466236272]\) \(2251439055699625/25088\) \(1292543151968768\) \([2]\) \(1360800\) \(2.4685\)  
52094.g2 52094j5 \([1, 0, 0, -634508, -195152240]\) \(-548347731625/1835008\) \(-94540299115429888\) \([2]\) \(680400\) \(2.1220\)  
52094.g3 52094j4 \([1, 0, 0, -132173, -15171191]\) \(4956477625/941192\) \(48490564185578312\) \([2]\) \(453600\) \(1.9192\)  
52094.g4 52094j2 \([1, 0, 0, -39148, 2976126]\) \(128787625/98\) \(5048996687378\) \([2]\) \(151200\) \(1.3699\)  
52094.g5 52094j1 \([1, 0, 0, -1938, 66304]\) \(-15625/28\) \(-1442570482108\) \([2]\) \(75600\) \(1.0234\) \(\Gamma_0(N)\)-optimal
52094.g6 52094j3 \([1, 0, 0, 16667, -1388607]\) \(9938375/21952\) \(-1130975257972672\) \([2]\) \(226800\) \(1.5727\)  

Rank

sage: E.rank()
 

The elliptic curves in class 52094.g have rank \(0\).

Complex multiplication

The elliptic curves in class 52094.g do not have complex multiplication.

Modular form 52094.2.a.g

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

\(\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 9 & 18 & 6 \\ 2 & 1 & 6 & 18 & 9 & 3 \\ 3 & 6 & 1 & 3 & 6 & 2 \\ 9 & 18 & 3 & 1 & 2 & 6 \\ 18 & 9 & 6 & 2 & 1 & 3 \\ 6 & 3 & 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.