Properties

Label 250470.b
Number of curves $2$
Conductor $250470$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 250470.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
250470.b1 250470b2 \([1, -1, 0, -264105, -52151225]\) \(1577505447721/838350\) \(1082702171811150\) \([2]\) \(3225600\) \(1.8346\)  
250470.b2 250470b1 \([1, -1, 0, -13635, -1105439]\) \(-217081801/285660\) \(-368920740024540\) \([2]\) \(1612800\) \(1.4880\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 250470.b have rank \(0\).

Complex multiplication

The elliptic curves in class 250470.b do not have complex multiplication.

Modular form 250470.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} - 4 q^{7} - q^{8} + q^{10} - 4 q^{13} + 4 q^{14} + q^{16} - 6 q^{17} + 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.