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Properties

Label 134862.bs
Number of curves $6$
Conductor $134862$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("bs1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 134862.bs have rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 - T\)
\(3\)\(1 - T\)
\(7\)\(1 + T\)
\(13\)\(1\)
\(19\)\(1 + T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(5\) \( 1 + 5 T^{2}\) 1.5.a
\(11\) \( 1 + 6 T + 11 T^{2}\) 1.11.g
\(17\) \( 1 + 17 T^{2}\) 1.17.a
\(23\) \( 1 - 6 T + 23 T^{2}\) 1.23.ag
\(29\) \( 1 - 6 T + 29 T^{2}\) 1.29.ag
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 134862.bs do not have complex multiplication.

Modular form 134862.2.a.bs

Copy content sage:E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} - q^{7} + q^{8} + q^{9} - 6 q^{11} + q^{12} - q^{14} + q^{16} + q^{18} - q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

Copy content 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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 6 & 9 & 18 \\ 2 & 1 & 6 & 3 & 18 & 9 \\ 3 & 6 & 1 & 2 & 3 & 6 \\ 6 & 3 & 2 & 1 & 6 & 3 \\ 9 & 18 & 3 & 6 & 1 & 2 \\ 18 & 9 & 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 134862.bs

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
134862.bs1 134862h6 \([1, 0, 0, -1653954078, -25890211391292]\) \(103665426767620308239307625/5961940992\) \(28777150437654528\) \([2]\) \(44789760\) \(3.5447\)  
134862.bs2 134862h5 \([1, 0, 0, -103372318, -404539467580]\) \(25309080274342544331625/191933498523648\) \(926426338075430879232\) \([2]\) \(22394880\) \(3.1981\)  
134862.bs3 134862h4 \([1, 0, 0, -20438103, -35447107671]\) \(195607431345044517625/752875610010048\) \(3633986770276989776832\) \([2]\) \(14929920\) \(2.9954\)  
134862.bs4 134862h3 \([1, 0, 0, -1888663, 30551273]\) \(154357248921765625/89242711068672\) \(430757520970665627648\) \([2]\) \(7464960\) \(2.6488\)  
134862.bs5 134862h2 \([1, 0, 0, -1341948, 560478996]\) \(55369510069623625/3916046302812\) \(18902007538829686908\) \([2]\) \(4976640\) \(2.4461\)  
134862.bs6 134862h1 \([1, 0, 0, -1318288, 582478064]\) \(52492168638015625/293197968\) \(1415210590724112\) \([2]\) \(2488320\) \(2.0995\) \(\Gamma_0(N)\)-optimal