Properties

Label 185150.bc
Number of curves $4$
Conductor $185150$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("bc1")
 
E.isogeny_class()
 

Elliptic curves in class 185150.bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
185150.bc1 185150co4 \([1, 1, 0, -2206340250, 39888289690250]\) \(513516182162686336369/1944885031250\) \(4498637259435727050781250\) \([2]\) \(189775872\) \(3.9451\)  
185150.bc2 185150co3 \([1, 1, 0, -139934000, 603840471500]\) \(131010595463836369/7704101562500\) \(17820055058609008789062500\) \([2]\) \(94887936\) \(3.5985\)  
185150.bc3 185150co2 \([1, 1, 0, -37572500, 9478025000]\) \(2535986675931409/1450751712200\) \(3355676866153111653125000\) \([2]\) \(63258624\) \(3.3958\)  
185150.bc4 185150co1 \([1, 1, 0, -24347500, -46053750000]\) \(690080604747409/3406760000\) \(7880042893900625000000\) \([2]\) \(31629312\) \(3.0492\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 185150.bc have rank \(1\).

Complex multiplication

The elliptic curves in class 185150.bc do not have complex multiplication.

Modular form 185150.2.a.bc

sage: E.q_eigenform(10)
 
\(q - q^{2} + 2 q^{3} + q^{4} - 2 q^{6} + q^{7} - q^{8} + q^{9} + 6 q^{11} + 2 q^{12} + 4 q^{13} - q^{14} + q^{16} + 6 q^{17} - q^{18} - 8 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.