Properties

Label 2904d
Number of curves $6$
Conductor $2904$
CM no
Rank $0$
Graph

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

Elliptic curves in class 2904d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2904.c5 2904d1 \([0, -1, 0, 81, -372]\) \(2048/3\) \(-85034928\) \([2]\) \(640\) \(0.20702\) \(\Gamma_0(N)\)-optimal
2904.c4 2904d2 \([0, -1, 0, -524, -3276]\) \(35152/9\) \(4081676544\) \([2, 2]\) \(1280\) \(0.55360\)  
2904.c2 2904d3 \([0, -1, 0, -7784, -261732]\) \(28756228/3\) \(5442235392\) \([2]\) \(2560\) \(0.90017\)  
2904.c3 2904d4 \([0, -1, 0, -2944, 59644]\) \(1556068/81\) \(146940355584\) \([2, 2]\) \(2560\) \(0.90017\)  
2904.c1 2904d5 \([0, -1, 0, -46504, 3875500]\) \(3065617154/9\) \(32653412352\) \([2]\) \(5120\) \(1.2467\)  
2904.c6 2904d6 \([0, -1, 0, 1896, 231948]\) \(207646/6561\) \(-23804337604608\) \([2]\) \(5120\) \(1.2467\)  

Rank

sage: E.rank()
 

The elliptic curves in class 2904d have rank \(0\).

Complex multiplication

The elliptic curves in class 2904d do not have complex multiplication.

Modular form 2904.2.a.d

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2q^{5} + q^{9} + 2q^{13} + 2q^{15} - 2q^{17} + 4q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.