Properties

Label 74256bw
Number of curves $2$
Conductor $74256$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bw1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 74256bw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
74256.b1 74256bw1 \([0, -1, 0, -7280, -236544]\) \(10418796526321/6390657\) \(26176131072\) \([2]\) \(143360\) \(0.94179\) \(\Gamma_0(N)\)-optimal
74256.b2 74256bw2 \([0, -1, 0, -5920, -329024]\) \(-5602762882081/8312741073\) \(-34048987435008\) \([2]\) \(286720\) \(1.2884\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 74256.2.a.bw

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.