Properties

Label 1288b
Number of curves $2$
Conductor $1288$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1288b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1288.f2 1288b1 \([0, -1, 0, -28, 84]\) \(-9826000/3703\) \(-947968\) \([2]\) \(160\) \(-0.14333\) \(\Gamma_0(N)\)-optimal
1288.f1 1288b2 \([0, -1, 0, -488, 4316]\) \(12576878500/1127\) \(1154048\) \([2]\) \(320\) \(0.20324\)  

Rank

sage: E.rank()
 

The elliptic curves in class 1288b have rank \(0\).

Complex multiplication

The elliptic curves in class 1288b do not have complex multiplication.

Modular form 1288.2.a.b

sage: E.q_eigenform(10)
 
\(q + 2q^{3} - q^{7} + q^{9} + 4q^{11} + 6q^{13} + O(q^{20})\)  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.