Properties

Label 1520.b
Number of curves $2$
Conductor $1520$
CM no
Rank $1$
Graph

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

Elliptic curves in class 1520.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1520.b1 1520i1 \([0, 1, 0, -921, -10346]\) \(5405726654464/407253125\) \(6516050000\) \([2]\) \(960\) \(0.62837\) \(\Gamma_0(N)\)-optimal
1520.b2 1520i2 \([0, 1, 0, 884, -44280]\) \(298091207216/3525390625\) \(-902500000000\) \([2]\) \(1920\) \(0.97495\)  

Rank

sage: E.rank()
 

The elliptic curves in class 1520.b have rank \(1\).

Complex multiplication

The elliptic curves in class 1520.b do not have complex multiplication.

Modular form 1520.2.a.b

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} - q^{5} - 2 q^{7} + q^{9} + 6 q^{13} + 2 q^{15} + 2 q^{17} + q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.