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Properties

Label 10830v
Number of curves $8$
Conductor $10830$
CM no
Rank $1$
Graph

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

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 10830v have rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 - T\)
\(3\)\(1 + T\)
\(5\)\(1 + T\)
\(19\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(7\) \( 1 - 4 T + 7 T^{2}\) 1.7.ae
\(11\) \( 1 + 11 T^{2}\) 1.11.a
\(13\) \( 1 + 2 T + 13 T^{2}\) 1.13.c
\(17\) \( 1 + 2 T + 17 T^{2}\) 1.17.c
\(23\) \( 1 + 23 T^{2}\) 1.23.a
\(29\) \( 1 + 10 T + 29 T^{2}\) 1.29.k
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 10830v do not have complex multiplication.

Modular form 10830.2.a.v

Copy content sage:E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{5} - q^{6} - 4 q^{7} + q^{8} + q^{9} - q^{10} - q^{12} - 2 q^{13} - 4 q^{14} + q^{15} + q^{16} + 6 q^{17} + q^{18} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.

Elliptic curves in class 10830v

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10830.q8 10830v1 \([1, 1, 1, 534, -14361]\) \(357911/2160\) \(-101619102960\) \([2]\) \(13824\) \(0.79393\) \(\Gamma_0(N)\)-optimal
10830.q6 10830v2 \([1, 1, 1, -6686, -193417]\) \(702595369/72900\) \(3429644724900\) \([2, 2]\) \(27648\) \(1.1405\)  
10830.q7 10830v3 \([1, 1, 1, -4881, 427503]\) \(-273359449/1536000\) \(-72262473216000\) \([2]\) \(41472\) \(1.3432\)  
10830.q4 10830v4 \([1, 1, 1, -104156, -12981481]\) \(2656166199049/33750\) \(1587798483750\) \([2]\) \(55296\) \(1.4871\)  
10830.q5 10830v5 \([1, 1, 1, -24736, 1279463]\) \(35578826569/5314410\) \(250021100445210\) \([2]\) \(55296\) \(1.4871\)  
10830.q3 10830v6 \([1, 1, 1, -120401, 15999599]\) \(4102915888729/9000000\) \(423412929000000\) \([2, 2]\) \(82944\) \(1.6898\)  
10830.q2 10830v7 \([1, 1, 1, -163721, 3402143]\) \(10316097499609/5859375000\) \(275659458984375000\) \([2]\) \(165888\) \(2.0364\)  
10830.q1 10830v8 \([1, 1, 1, -1925401, 1027521599]\) \(16778985534208729/81000\) \(3810716361000\) \([2]\) \(165888\) \(2.0364\)