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Properties

Label 1526e
Number of curves $2$
Conductor $1526$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 1526e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1526.f2 1526e1 \([1, 1, 1, 50, 363]\) \(13806727199/58622816\) \(-58622816\) \([5]\) \(400\) \(0.17311\) \(\Gamma_0(N)\)-optimal
1526.f1 1526e2 \([1, 1, 1, -5060, -142437]\) \(-14327836828683841/215407353686\) \(-215407353686\) \([]\) \(2000\) \(0.97783\)  

Rank

sage: E.rank()
 

The elliptic curves in class 1526e have rank \(1\).

Complex multiplication

The elliptic curves in class 1526e do not have complex multiplication.

Modular form 1526.2.a.e

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + q^{7} + q^{8} - 2 q^{9} + q^{10} - 3 q^{11} - q^{12} - 6 q^{13} + q^{14} - q^{15} + q^{16} - 2 q^{17} - 2 q^{18} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.