Properties

Label 15631b
Number of curves $2$
Conductor $15631$
CM no
Rank $1$
Graph

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

Elliptic curves in class 15631b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15631.b1 15631b1 \([0, -1, 1, -3103, -99233]\) \(-28094464000/20657483\) \(-2430332217467\) \([]\) \(16128\) \(1.0760\) \(\Gamma_0(N)\)-optimal
15631.b2 15631b2 \([0, -1, 1, 25317, 1539180]\) \(15252992000000/17621717267\) \(-2073177414745283\) \([]\) \(48384\) \(1.6253\)  

Rank

sage: E.rank()
 

The elliptic curves in class 15631b have rank \(1\).

Complex multiplication

The elliptic curves in class 15631b do not have complex multiplication.

Modular form 15631.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2 q^{4} - 2 q^{9} - q^{11} + 2 q^{12} - 2 q^{13} + 4 q^{16} - 6 q^{17} + 7 q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.