Properties

Label 74256.cd
Number of curves $6$
Conductor $74256$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("cd1")
 
E.isogeny_class()
 

Elliptic curves in class 74256.cd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
74256.cd1 74256dd6 \([0, 1, 0, -649264, 201002900]\) \(7389727131216686257/6115533215337\) \(25049224050020352\) \([4]\) \(786432\) \(2.0750\)  
74256.cd2 74256dd4 \([0, 1, 0, -49504, 1642676]\) \(3275619238041697/1605271262049\) \(6575191089352704\) \([2, 4]\) \(393216\) \(1.7285\)  
74256.cd3 74256dd2 \([0, 1, 0, -26384, -1640364]\) \(495909170514577/6224736609\) \(25496521150464\) \([2, 2]\) \(196608\) \(1.3819\)  
74256.cd4 74256dd1 \([0, 1, 0, -26304, -1650828]\) \(491411892194497/78897\) \(323162112\) \([2]\) \(98304\) \(1.0353\) \(\Gamma_0(N)\)-optimal
74256.cd5 74256dd3 \([0, 1, 0, -4544, -4252428]\) \(-2533811507137/1904381781393\) \(-7800347776585728\) \([2]\) \(393216\) \(1.7285\)  
74256.cd6 74256dd5 \([0, 1, 0, 180336, 12766932]\) \(158346567380527343/108665074944153\) \(-445092146971250688\) \([4]\) \(786432\) \(2.0750\)  

Rank

sage: E.rank()
 

The elliptic curves in class 74256.cd have rank \(0\).

Complex multiplication

The elliptic curves in class 74256.cd do not have complex multiplication.

Modular form 74256.2.a.cd

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.