Properties

Label 15210.v
Number of curves $4$
Conductor $15210$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("v1")
 
E.isogeny_class()
 

Elliptic curves in class 15210.v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15210.v1 15210v3 \([1, -1, 0, -315639, 65594205]\) \(988345570681/44994560\) \(158324327278940160\) \([2]\) \(290304\) \(2.0622\)  
15210.v2 15210v1 \([1, -1, 0, -49464, -4196880]\) \(3803721481/26000\) \(91487337786000\) \([2]\) \(96768\) \(1.5129\) \(\Gamma_0(N)\)-optimal
15210.v3 15210v2 \([1, -1, 0, -19044, -9325692]\) \(-217081801/10562500\) \(-37166730975562500\) \([2]\) \(193536\) \(1.8595\)  
15210.v4 15210v4 \([1, -1, 0, 171081, 249282333]\) \(157376536199/7722894400\) \(-27174886486861838400\) \([2]\) \(580608\) \(2.4088\)  

Rank

sage: E.rank()
 

The elliptic curves in class 15210.v have rank \(1\).

Complex multiplication

The elliptic curves in class 15210.v do not have complex multiplication.

Modular form 15210.2.a.v

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{5} + 4 q^{7} - q^{8} - q^{10} - 6 q^{11} - 4 q^{14} + q^{16} + 6 q^{17} - 2 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.