Properties

Label 2925.d
Number of curves $8$
Conductor $2925$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2925.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2925.d1 2925g7 \([1, -1, 1, -29250005, 60896057622]\) \(242970740812818720001/24375\) \(277646484375\) \([2]\) \(73728\) \(2.5434\)  
2925.d2 2925g5 \([1, -1, 1, -1828130, 951838872]\) \(59319456301170001/594140625\) \(6767633056640625\) \([2, 2]\) \(36864\) \(2.1969\)  
2925.d3 2925g8 \([1, -1, 1, -1784255, 999662622]\) \(-55150149867714721/5950927734375\) \(-67784786224365234375\) \([2]\) \(73728\) \(2.5434\)  
2925.d4 2925g3 \([1, -1, 1, -117005, 14142372]\) \(15551989015681/1445900625\) \(16469711806640625\) \([2, 2]\) \(18432\) \(1.8503\)  
2925.d5 2925g2 \([1, -1, 1, -25880, -1348878]\) \(168288035761/27720225\) \(315750687890625\) \([2, 2]\) \(9216\) \(1.5037\)  
2925.d6 2925g1 \([1, -1, 1, -24755, -1492878]\) \(147281603041/5265\) \(59971640625\) \([2]\) \(4608\) \(1.1571\) \(\Gamma_0(N)\)-optimal
2925.d7 2925g4 \([1, -1, 1, 47245, -7637628]\) \(1023887723039/2798036865\) \(-31871388665390625\) \([2]\) \(18432\) \(1.8503\)  
2925.d8 2925g6 \([1, -1, 1, 136120, 66792372]\) \(24487529386319/183539412225\) \(-2090628617375390625\) \([2]\) \(36864\) \(2.1969\)  

Rank

sage: E.rank()
 

The elliptic curves in class 2925.d have rank \(0\).

Complex multiplication

The elliptic curves in class 2925.d do not have complex multiplication.

Modular form 2925.2.a.d

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} + 3 q^{8} - 4 q^{11} - q^{13} - q^{16} + 2 q^{17} - 4 q^{19} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 8 & 16 & 16 & 8 \\ 2 & 1 & 2 & 2 & 4 & 8 & 8 & 4 \\ 4 & 2 & 1 & 4 & 8 & 16 & 16 & 8 \\ 4 & 2 & 4 & 1 & 2 & 4 & 4 & 2 \\ 8 & 4 & 8 & 2 & 1 & 2 & 2 & 4 \\ 16 & 8 & 16 & 4 & 2 & 1 & 4 & 8 \\ 16 & 8 & 16 & 4 & 2 & 4 & 1 & 8 \\ 8 & 4 & 8 & 2 & 4 & 8 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.