Properties

Label 15631c
Number of curves $4$
Conductor $15631$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 15631c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15631.a4 15631c1 \([1, -1, 1, 28631, -2132504]\) \(22062729659823/29354283343\) \(-3453502081020607\) \([4]\) \(64512\) \(1.6673\) \(\Gamma_0(N)\)-optimal
15631.a3 15631c2 \([1, -1, 1, -177414, -20758972]\) \(5249244962308257/1448621666569\) \(170428890450176281\) \([2, 2]\) \(129024\) \(2.0139\)  
15631.a1 15631c3 \([1, -1, 1, -2614429, -1626264454]\) \(16798320881842096017/2132227789307\) \(250854467184179243\) \([2]\) \(258048\) \(2.3605\)  
15631.a2 15631c4 \([1, -1, 1, -1037119, 390180018]\) \(1048626554636928177/48569076788309\) \(5714103315067765541\) \([2]\) \(258048\) \(2.3605\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 15631.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} + 2q^{5} + 3q^{8} - 3q^{9} - 2q^{10} - q^{11} - 6q^{13} - q^{16} + 2q^{17} + 3q^{18} + 8q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.