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Properties

Label 124950.dl
Number of curves $8$
Conductor $124950$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("dl1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 124950.dl have rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 + T\)
\(3\)\(1 - T\)
\(5\)\(1\)
\(7\)\(1\)
\(17\)\(1 + T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(11\) \( 1 + 11 T^{2}\) 1.11.a
\(13\) \( 1 - 2 T + 13 T^{2}\) 1.13.ac
\(19\) \( 1 - 4 T + 19 T^{2}\) 1.19.ae
\(23\) \( 1 + 23 T^{2}\) 1.23.a
\(29\) \( 1 - 6 T + 29 T^{2}\) 1.29.ag
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 124950.dl do not have complex multiplication.

Modular form 124950.2.a.dl

Copy content sage:E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} - q^{8} + q^{9} + q^{12} + 2 q^{13} + q^{16} - q^{17} - q^{18} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 124950.dl

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
124950.dl1 124950co7 \([1, 0, 1, -16292335876, 799835059326398]\) \(260174968233082037895439009/223081361502731896500\) \(410082798428670388927007812500\) \([2]\) \(254803968\) \(4.6089\)  
124950.dl2 124950co8 \([1, 0, 1, -10700210876, -421512382673602]\) \(73704237235978088924479009/899277423164136103500\) \(1653110774341210131885492187500\) \([2]\) \(254803968\) \(4.6089\)  
124950.dl3 124950co5 \([1, 0, 1, -10668679376, -424145651885602]\) \(73054578035931991395831649/136386452160\) \(250714526721435000000\) \([2]\) \(84934656\) \(4.0596\)  
124950.dl4 124950co6 \([1, 0, 1, -1246273376, 6486275826398]\) \(116454264690812369959009/57505157319440250000\) \(105709753960544155816406250000\) \([2, 2]\) \(127401984\) \(4.2623\)  
124950.dl5 124950co4 \([1, 0, 1, -700119376, -5928252845602]\) \(20645800966247918737249/3688936444974392640\) \(6781245059606129995365000000\) \([2]\) \(84934656\) \(4.0596\)  
124950.dl6 124950co2 \([1, 0, 1, -666799376, -6627173165602]\) \(17836145204788591940449/770635366502400\) \(1416632503650638400000000\) \([2, 2]\) \(42467328\) \(3.7130\)  
124950.dl7 124950co1 \([1, 0, 1, -39599376, -114328365602]\) \(-3735772816268612449/909650165760000\) \(-1672178630492160000000000\) \([2]\) \(21233664\) \(3.3664\) \(\Gamma_0(N)\)-optimal
124950.dl8 124950co3 \([1, 0, 1, 284976624, 777775826398]\) \(1392333139184610040991/947901937500000000\) \(-1742495547577148437500000000\) \([2]\) \(63700992\) \(3.9157\)