↑

Properties

Label 24150.w
Number of curves $2$
Conductor $24150$
CM no
Rank $2$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("w1")
 
E.isogeny_class()
 

Elliptic curves in class 24150.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
24150.w1 24150z1 \([1, 0, 1, -6126, 175648]\) \(1626794704081/83462400\) \(1304100000000\) \([2]\) \(73728\) \(1.0826\) \(\Gamma_0(N)\)-optimal
24150.w2 24150z2 \([1, 0, 1, 3874, 695648]\) \(411664745519/13605414480\) \(-212584601250000\) \([2]\) \(147456\) \(1.4292\)  

Rank

sage: E.rank()
 

The elliptic curves in class 24150.w have rank \(2\).

Complex multiplication

The elliptic curves in class 24150.w do not have complex multiplication.

Modular form 24150.2.a.w

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.